Simulation of dendritic grain structures with Cellular Automaton–Parabolic Thick Needle model

Abstract

This article presents advances and computing optimizations on the CAPTN model which couples the Cellular Automaton (CA) and the Parabolic Thick Needle (PTN) methods. This optimized CAPTN model, which is developed in 2D for now, is evaluated on its ability to reproduce two physical quantities developed during directional growth in a constant temperature gradient G with isotherm velocity vL: the interdendritic primary spacing and the grain boundary orientation angle between two grains of different orientations. It is shown that the CAPTN model can reproduce selection between primary branches and creation of new branches from tertiary branches as long as cell size is sufficiently small to model solute interactions between branches. In these conditions, simulations converge toward a distribution of primary branches which depends on the history of the branching events, as has been observed in experimental studies. Average primary spacing obtained tends to decrease with G and vL, in agreement with the theoretical G−bvL−c power law. Contrary to the classical CA model, the grain boundary orientation angle obtained in CAPTN simulations is stable with cell size and in good agreement with previous phase field studies for various gradients. Moreover, the grain boundary orientation angle is found to follow an exponential law with the ratio G/vL.