Effect of clustering of precipitates on grain growth

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.