Grain growth inhibition by spherical particles with a distribution of sizes

The inhibition of primary grain growth in 3% Si-Fe by particles and/or solutes is a requirement for obtaining complete secondary recrystallization in this alloy. Past theoretical treatments of grain growth inhibition by particles have been limited mainly to spherical particles of uniform size. In the present work, a method is derived for estimating the inhibiting strength of a system of spherical particles with a distribution of sizes from a knowledge of the particle size histogram and the volume fraction of the particles. The method is illustrated with data from the literature on manganese sulfide particles in 3% Si-Fe and carbides in ferrite. The calculated inhibition strengths of manganese sulfide particles in 3% Si-Fe correlated well with the primary grain sizes attained in a laboratory-simulated box anneal.