Effect of clustering of precipitates on grain growth
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2/12/04
6:30 PM
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Effect of Clustering of Precipitates on Grain Growth E. FLORES, J.M. CABRERA, and J.M. PRADO The present work shows that clustering of particles promotes deviation in the classical mathematical expressions describing the grain growth control by second-phase particles. On the basis of experimental results and theoretical laws, a semiempirical expression to predict the limiting grain size is presented. The latter expression takes account of agglomeration phenomena and can be extended to large volume fractions of particles, conditions under which classical theories clearly fail. The equation remains valid as far as the nucleation of precipitates takes place at random. From a practical point of view, it is shown that volume fractions larger than 0.12 cannot significatively control the grain size because of the increased probability for clustering.
I. INTRODUCTION
ONE of the most important and frequent ways of controlling the microstructure of engineering alloys, and therefore their mechanical properties, is to refine the grain size. This in turn can be achieved by pinning the grain boundaries by second-phase particles. Size and volume fraction of particles as well as the homogeneity of the nucleation sites are the factors that determine the efficiency of particles in governing the grain size. Since the Zener’s expression,[1] several equations have been proposed to relate the grain size to some characteristics of the particles (see a complete review in Reference 2). In general, most theories maintain the original trends established by Zener, that is, the grain size in the presence of particles follows a critical grain size Rcrit inversely proportional to the volume fraction of particles and directly proportional to the particle size. The main differences between the diverse theories stay on the proportionality constant. Most theoretical models[2] fit experimental data with high accuracy up to volume fractions of approximately 0.02. Beyond this value, strong deviations are usually observed. It is worth noting here that most of the models assume that particles are distributed at random, and they do not contact among themselves, i.e., they are isolated. Nevertheless, there is enough experimental and theoretical evidence[3–8] showing that under certain circumstances, single particles are frequently found in contact with each other, connected, and forming clusters. Clustering, on the other hand, is a usual phenomenon in precipitation processes involved in certain chemical reactions.[9] In particular, the nonuniform distribution of particles seems to be a common feature in steels, especially in microalloyed steels, although most authors have not paid full attention to this phenomenon. It seems clear that the precipitation in clusters may promote a clear deviation of the hypothesis of homogeneous distribution assumed in many of the theoretical models.[2] In many of the grain growth theories,[2] the particle distribution is simply characterized by the average radius of its E. FLORES, Professor, is
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