Comparison of analytical models with cellular automata simulation of recrystallization in two dimensions

Abstract

Cellular automata simulation of recrystallization in two dimensions is carried out. The simulated microstrutural evolution is compared in detail with the predictions from mathematically exact analytical theories considering both kinetic and geometrical aspects. Very good agreement is observed between the cellular automata simulation and the theoretical results. Moreover, the simulated data is used to test new expressions recently derived to describe the evolution of the interfaces between recrystallized grains. This work focuses on recrystallization but its results are applicable to any nucleation and growth transformation

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

“…In this regard, computer simulation of microstructural evolution can be an invaluable tool since it can simulate situations beyond analytical treatment. Compared to other simulation methods, cellular automata [17][18][19][20][21][22][23][24][25][26][27][28][29][30] is a convenient choice for phase transformations in general and recrystallization in particular 23 . Computer simulation aims at describing transformation in complex situations for which there is no analytical theory.…”

“…Interestingly, this basic or minimum validation of the simulation has been rarely reported in published papers 23 . In previous papers 28,29 , present authors carried out cellular automata (CA) simulation of phase transformation/recrystallization in two dimensions (2D). Earliest computer simulations of microstructural evolution were usually performed in two dimensions.…”

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.…”

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

“…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.…”