Reorganization of cellular space during the modeling of the microstructure evolution by frontal cellular automata

Abstract The prediction of the microstructure evolution is one of the most significant problems in materials science. The objective of this paper is development of principles of the cellular space reorganization and their implementation into the three-dimensional frontal cellular automata (FCA) for modeling of the microstructure evolution during the multi-stage deformation. Motivation for the reorganization and principles governing this process are presented in the paper. The FCA cells do not keep the form of undistorted cubes during the simulation, but they get deformed. That leads to the necessity of space reorganization. Different conditions on the boundaries of the cellular space are taken into consideration as they are closely connected with the developed algorithms of the reorganization. These two variants of the reorganization are described in detail. The first one can be used when cellular space can be reduced; and the second one, when the reduction of modeled volume is not acceptable. A short description of frontal cellular automata is presented in this paper. The model consists of two parts: deformation and microstructure evolution. The independence of the grain growing from the shape and the sizes of the cell is ensured by so-called “virtual front tracking” algorithm. The microstructural part of the model simulates two phenomena: nucleation and growth of new grains. In this paper only static recrystallization is considered. When the recrystallization is simulated, the nucleation and the grain boundary migration depend on the deformation parameters such as: temperature, strain, strain rate, dislocation density and crystallographic orientation. This phenomenon, along with the deformation, can be modeled over a wide range of multi-stage deformation processes. The process of flat rolling is chosen as the simplest example. The data needed for the FCA simulation is received from the simple numerical calculations. The results of the simulation of the microstructure evolution obtained during the last five passes of the flat rolling are also presented in the paper.