Modeling and Simulation of Nucleation and Growth Transformations with Nucleation on Interfaces of Kelvin Polihedra Network

Abstract

Nucleation is a phenomenon associated to the start of the new phase, from a primary phase, named matrix. Growth is the increase in size of this new phase over time. In metallic materials, the nucleation may take place on the grain boundaries of the primary phase. A network of Kelvin polyhedra was used in this paper to represent the grains. A computer simulation was performed in which nucleation took places at the faces, edges and vertices of this polyhedral network. The Causal cone method was employed in the simulations. The results of the present computational simulations were compared with the classical Johnson Mehl-Avrami-Kolmogorov (JMAK) as well as with Cahn model for nucleation at the grain boundaries. JMAK theory considers nuclei to be uniform randomly located within the matrix. Cahn analytical model specifies that nucleation takes place on random planes. For a small number of nuclei, the simulations approached the JMAK model whereas as the number of nuclei increased the simulation results agree with Cahn's theory. Reasons for this are fully discussed.

Computational simulation of gliomas using stochastic methods

“…Another specific advantage for this work was to have a discrete model already validated by CCM prepared to simulate nucleation and growth. The base of the computational code whose Causal Cone Method was previously implemented and publicized in other works of international journals (Alves et al 2018;da Fonseca et al 2018;Ventura et al 2018) was also used to develop part of the numerical model proposed in this study. At each iteration a new radius value is calculated, thus, the glioma evolves as a function of the discrete time also known as step.…”

Kinetics of Grain-Boundary Nucleated Transformations in Rectangular Geometries and One Paradox Relating to Cahn's Model

“…microstructural descriptors [24][25][26][27][28][29], grain-size distribution functions [30][31][32][33][34][35], and other characteristics [36,37]. Double-logarithmic VF plots, together with the corresponding temporal behavior of the Avrami exponent, provide information on the mechanisms of nucleation and growth.…”