Cellular automata simulation of site-saturated and constant nucleation rate transformations in three dimensions

Abstract

Microstructural evolution in three dimensions of nucleation and growth transformations is simulated by means of cellular automata. Two types of nucleation are considered: site-saturated nucleation and constant nucleation rate. The simulated microstrutural evolution agrees very well with exact analytical expressions. The simulated data also gives very good agreement with expressions derived to describe the evolution of the interfaces between transformed grains.

Simulation of recrystallization in iron single crystals

“…Interestingly, this important, but non-obvious point is seldom ever mentioned in published CA simulations. An in-depth investigation of CA grain shape in 2-d and 3-d may be found in Rios et al 28,30 . The theoretical microstructural path in extended space is given by S VE = C (V VE ) q (10) where q = 2/3 for site-saturated reactions.…”

“…Therefore, it is not surprising that CA is the choice of many researchers simulating recrystallization, including Gottstein 17,18 and Raabe 19,20 and many others [21][22][23][24][25][26] . We too have published a series of papers using CA simulations 15,[27][28][29][30][31] . In those papers CA simulation was shown to be geometrically sound in 2-d 28 and 3-d 30 by comparing the results with exact analytical theory available for recrystallization of randomly located nuclei.…”

“…We too have published a series of papers using CA simulations 15,[27][28][29][30][31] . In those papers CA simulation was shown to be geometrically sound in 2-d 28 and 3-d 30 by comparing the results with exact analytical theory available for recrystallization of randomly located nuclei. Moreover, we also used CA simulations to study the influence of non-randomness of nuclei distribution 15,27,29,31 .…”

Inhomogeneous Poisson point process nucleation: comparison of analytical solution with cellular automata simulation

“…However, this good agreement can only be obtained if the appropriate shape factor is used, namely, α = 1 (CA shape) instead of α = π (spherical shape) in Equations 7-12. It is worth mentioning that a full derivation and discussion of the shape factor, α = 1, was carried out in a previous work 21 .…”

“…In previous papers [18][19][20][21][22][23][24] , cellular automata (CA) simulation of phase transformation/recrystallization in 2-d and 3-d were carried out and compared with KJMA analytical solutions. The purpose of the present paper is to simulate phase transformations/recrystallization in by cellular automata (CA) in order to compare the simulation with the analytical solution by Rios and Villa.…”