Abstract
A new model is presented to predict the critical grain radius ( R c ) as a function of the particle radius ( r) and of the volume fraction of the particles (ƒ). The result is R c = r 6ƒ , eight times less than Zener's, and was found to agree satisfactorily with the experimental results of Tweed, Hansen and Ralph [ Metall. Trans. 14A, 2235 (1983)]. The same expression is used to predict grain growth in systems in which the particles are coarsening and dissolving, such as Fe 3C/ferrite and NbC/austenite. Finally, abnormal growth in the presence of particles is considered. The circumstances in which abnormal or normal growth may occur are determined in relation to the maximum grain size and to the mean grain size of a grain assembly. The theoretical predictions are summarized in a grain growth mechanism map.
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