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Prediction of the microstructure and properties is one of the most important problems in materials science. There are different methods that are used for modeling of the microstructure evolution, among them are the front tracking method (Thompson et al., 1987; Frost et al., 1988), the phase-field models (Fan & Chen, 1997), the cellular automata (CA) models (Davies, 1997), vertex models (Weygand at al., 2001), Monte Carlo Potts models (Holm at al., 2001) and the finite element method (FEM) based models (Bernacki at al. 2007). Application of CA models, for simulation of the different phenomena in materials, has increased significantly in the resent years. CA approach is used for modeling of solidification (Rappaz & Gandin, 1993; Raabe, 2004), dynamic and static recrystallization (Kumar et al., 1998; Hurley & Humphreys, 2003; Qian & Guo, 2004), phase transformation (Das et al., 2002), grain refinement (Svyetlichnyy et al., 2008), micro-shear band and shear band propagation. The main asset of CA based methods is their ability for a close correlation between the microstructure and the mechanical properties during both microand mesoscale simulation. The joint methods based on CA and FEM improve accuracy of the coupled phenomena simulation during the forming processes. CA based models have been developed and are being used mostly as two-dimensional (2D) versions. However, threedimensional (3D) models have been published as well. The 2D CA models are simpler and faster. They also include less elements and connections. They are based on less complicated algorithms. They are also simpler for design, implementation and more useful for visualization. However, there are some problems which have been solved in the 2D CA, but are still unsolved in 3D CA. Microstructure evolution is in general the three-dimensional problem and the results obtained by 2D CA cannot always be directly transferred to a real 3D process. However, the 3D models require significantly more memory and time for the calculation. This is because they have more cells and each cell has more neighbors. The memory and also the processing time problems can be potentially solved by parallelization using several processors or computers working in the network. Another approach that has been applied recently, along with the parallelization, is based on development of different algorithms capable of using appropriate properties of the special CA types. One of these algorithms, known as the frontal CA (FCA) and developed for simulation of the microstructure evolution, is described by Svyetlichnyy (2010).

Modeling of Macrostructure Formation during the Solidification by using Frontal Cellular Automata