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A Modified Cellular Automaton Model for the Simulation of
Dendritic Growth in Solidification
*
Li Qingsong
School of Mechanical and Electrical Engineering, East China Jiaotong University
Nanchang(330013)
E-mail:chinsunglee@gmail.com
Abstract
A modified cellular automaton model (mCA) was developed in order to simulate the evolution of
dendritic microstructures in solidification of alloys. The mCA model numerically calculated solute
redistribution both in the solid and liquid phases, the curvature of dendrite tips and the growth
anisotropy. This modeling takes account of thermal, curvature and solute diffusion effects. Therefore, it
can simulate microstructure formation both on the scale of the dendrite tip length. This model was then
applied for simulating dendritic solidification of an Al-7%Si alloy. Both directional and equiaxed
dendritic growth has been performed to investigate the growth anisotropy and cooling rate on dendrite
morphology. Furthermore, the competitive growth and selection of dendritic crystals have also
investigated.
Keywords: dendritic growth, solidification, probabilistic model, mCA
1. Introduction
The Cellular Automaton (CA) technique
[1]
has successfully applied to generate
realistic-looking microstructures because it based on the consideration of physical mechanisms of
nucleation, growth kinetics and crystallographic orientation competition. However, the original
CA is only related to the local temperature in the solidifying area for a given alloy composition.
This implies that only the thermal effect is considered in the CA model. Therefore, it is unable to
describe the dendritic features such as the side branches, which controlled by solute redistribution
and curvature effect.
Phase field models
[2, 3]
offer an opportunity for predicting dendritic growth with description
of detail features of dendrite and better understanding of the dynamics of dendritic pattern
selection, however, phase field models are limited to calculate just a few dendrites within a small
domain due to the large computational capacity needed. There exists a gap between the CA model
and the phase field model in predicting microstructure formation in length-scale.
The CA algorithm was further modified by Nastac
[4]
, Zhu and Hong
[5]
and Yao et al.
[6]
, who
incorporated the effects of solute redistribution and dendrite tip capillarity, in order to simulate the
concentration field and dendrite morphology on a mesoscopic level. Within this new model, the
thermal, solute and capillary effects are all applied to nucleation and growth, to simulate the
dendritic solidification microstructures in a much bigger domain. Thus, it can be used to study the
interactions of dendritic growth in many grains in a solidifying mushy region. However, it should
be noted that this method is also limited to a smaller domain compared with original CA algorithm
due to a much finer mesh is required for the solute field calculation.
2. Model Description
2.1 The governing equations
If sub-headings Neglecting the effect of convection, the solidification process is controlled by
thermal and solute diffusion. The equations that describe the physics of these processes are:
*
Supported by Graduate student innovation project foundation of Jiangxi Province (Grant No.YC07B023).