Microstructural Dynamic Study of Grain Growth

The complete prediction of microstructural development in polycrystalline solids as a function of time and temperature is a major objective in materials science, but has not yet been possible primarily due to the complexity of the grain interactions. The evolution of the polycrystalline structure depends upon the precise specification of the coordinates of the grain boundary network, the crystallographic orientations of the grains, and the postulated microscopic mechanisms by which elements of the boundaries are assumed to move. Therefore, a general analytical solution to this multivariate problem has not yet been developed. Recently, we have been able to successfully incorporate these aspects of the grain interactions, and have developed a computer model which predicts the main features of the microstructure from first principles. The polycrystal is mapped onto a discrete lattice by dividing the material into small area or volume elements, and placing the centers of these elements on lattice points. Interactions and dynamics are then defined for the individual elements which are analagous to those postulated in continuous systems. This discrete model preserves the topological features of real materials, and can be studied by computer simulation using Monte Carlo techniques. In this paper we report the application of the Monte Carlo method to the metallurgical phenomenon of grain growth with isothermal annealing. Extension of the model to treat primary recrystallization is presented elsewhere.