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

Abstract

A multiscale numerical model, coupling the Cellular Automaton (CA) method to the Parabolic Thick Needle (PTN) method, is developed to compute dendritic microstructures. It is applied to directional solidification of bi-crystals under a frozen temperature approximation with fixed temperature gradient and fixed cooling rate. A dendritic branch is modeled as a cylinder headed by a parabolic tip. Its kinetics is computed using the PTN method from the composition field in the liquid in the vicinity of the parabola. This dendritic branch takes part in the definition of a grain envelope by its integration in a CA growth algorithm. The so-called Cellular Automaton – Parabolic Thick Needle (CAPTN) model can simulate the growth of dendritic grains while accounting for non-steady diffusion fields. The PTN method is implemented using Finite Element (FE) method on a heterogeneous mesh. An adaptive FE mesh strategy is developed to optimize computational time. The grain boundary orientation angle of a diverging bi-crystal configuration is investigated at steady state and compared to the Phase-Field (PF) method and the classical CA method. It is shown that contrary to the CA method, the CAPTN model is in good agreement with data deduced from PF simulations, demonstrating the interest of this coupling in the modeling of dendritic growth.