Journal of University of Science and Technology Beijing
Volume 11, Number 6, December 2004, Page 517
Corresponding author: Wanhua Yu, E-mail: wanhua.yu@mater.ustb.edu.cn
Materials
Cellular automata modelling of austenite grain coarsening during reheating
I. Normal grain coarsening
Wanhua Yu
1)
, E.J. Palmiere
2)
, S.P. Banks
3)
, and Jingtao Han
1)
1) Materials Science and Engineering School, University of Science and Technology Beijing, Beijing 100083, China
2) Department of Engineering Materials, University of Sheffield, Sheffield S1 3JD, UK
3) Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield S1 3JD, UK
(Received 2004-04-19)
Abstract: A two-dimensional cellular automaton (CA) model has been developed for the description of the normal grain coarsening
process. The probabilistic CA method incorporating Moore’s definition of the neighbourhood is used to simulate the normal grain
coarsening process with a new transition rule. The model simulates the grain coarsening process in as much detail that is possible,
from the point of initial nucleation to subsequent coarsening with computational times. The unique result is that the grain coarsening
speed can be controlled by the specific method, this result is vital to model the grain coarsening quantitatively. In order to make this
model valid, experimental work has been done to provide solid evidence for this model. Comparison of the modelling result and the
experimental result has been carried out.
Key words: computer simulation; grain growth; microstructure; reheating
1 Introduction
The thermomechanical rolling process can be
briefly divided into the following general categories:
reheating, rough rolling, finish rolling and runout table
cooling. During each of these stages, a great deal of
physical metallurgy related to the process occurs
which influences the microstructure and subsequent
mechanical properties of the final product. Grain
coarsening represents one of these processes occurring
during reheating and in the delay between the rolling
passes after recrystallization. At present, the evolution
of microstructure is oversimplified because only the
mean grain size is considered, and therefore it is dif-
ficult to provide information on the dynamic evolution
of the microstructure and its inhomogeneous distribu-
tion across a given cross-section.
Due to the difficulty of directly incorporating the
topological features into the empirical models of grain
coarsening, together with the difficulty of giving a
space-time description of grain distributions, there has
been increasing interest in using computer simulations
to study the grain coarsening in single phase materials.
A variety of models have therefore been put forward.
These have included the continuum field model [1, 2],
the Monte Carlo (MC) model [3-5], the Vertex model
[6], and the cellular automaton (CA) model [7]. Al-
though these methods can give graphical description
of the dynamical microstructural evolution, different
methods put forward different grain coarsening expo-
nents. Among these, the Exxon group using the Monte
Carlo method [3] predicted the grain coarsening ki-
netics to be 0.410.03. Fan and Chen [1] using the
continuum field model put forward the n
value of 0.5.
Liu [7
] using the CA method got the n value of 0.45.
A common feature of all these models is that all of
them describe grain kinetics as a single value or a
range. However, Hu [8] presented a detailed study of
isothermal grain coarsening in zone-refined iron in the
temperature range of 550-850C, which showed that n
increases with temperature from approximately 0.25
to 0.5, meaning that n is temperature dependent.
Liu [7] applied the CA method to simulate normal
grain coarsening using Von Neumann’s definition of
neighbouring cells with deterministic transformation
rules. Raabe
[9] showed some consecutive 2D sections
from a 3D grain coarsening simulation of a recrystal-
lized aluminum single crystal. All equations of motion
were simultaneously integrated using a weighted sto-
chastic sampling integration scheme.
Building on these, it has been tried to simulate the
grain coarsening process during reheating using the
CA method. This paper reports on the first stage of the
work which is to simulate the normal grain coarsening
behaviour of austenite [10, 11]. The model uses
Moore’s [12] definition of a neighbourhood to simu-
late the grain coarsening process with a new nuclea-