Computer simulation of site saturation and constant nucleation rate transformations on a network of Kelvin polyhedra

A crucial step of transformations in solids is that of nucleation. To model nucleation, one must specify nuclei location in space as well as how nuclei appear as a function of time. In the classical theory of Johnson–Mehl–Avrami–Kolmogorov (JMAK), there are two essential nucleation modes. One is site-saturation in which all nucleation sites are exhausted early in the transformation. Another is the so-called constant nucleation rate. JMAK theory considers that nuclei are located uniform randomly within the matrix both in the case of site-saturation and constant nucleation rate. Nonetheless, it is usually common in polycrystals to observe nucleation taking place on the grain surfaces, edges, and vertices. Cahn proposed analytical expression for such situations. In this work, we conduct a computer simulation considering that grains can be represented by a network of Kelvin polyhedra. We restrict nucleation to the grain boundaries of the Kelvin network. Grain boundary nucleation can be either site-saturated or a constant nucleation rate. We compare the effect of these two nucleation modes. JMAK theory and Cahn’s theory are applied to the simulated results. The microstructures are characterized by several quantitative metallographic parameters. We observed that the two nucleation modes exhibited similar behavior.