Prediction of phase transformation and microstructure in steel using cellular automaton technique
Introduction
Several mathematical models are available to predict the kinetics of decomposition of austenite. These use either the additivity principle of Scheil along with the Avrami equation [1], [2] or the classical theory of thermodynamics and kinetics [3], [4], [5], [6]. Neither model, however, addresses the evolution of microstructure during phase transformation––a gap attempted to be bridged in recent times by the use of Cellular Automata (CA) [7]. In this approach, metallurgical rules are prudently interwoven in the mathematical model in such a manner that the model generates information on the phase transformation and at the same time permits a pictorial view of the transformation to be drawn.
Section snippets
The computational domain
The cellular automaton used in this study has been developed in two dimensions on a square grid, representing an austenite grain. The computational domain is one austenite grain with an ‘average’ grain size.
The total grain surface area in a grain has been calculated after a stereological correction on the grain size. A spherical volume, which is the nearest regular shape to the actual tetrakaidecaheadral shape of the austenite grain, has been considered as the grain volume. A cube with the same
Experimental
Experiments were carried out to validate the austenite to ferrite transformation kinetics. Small cylindrical (6 mm diameter × 20 mm length) samples of low carbon steel with 0.19% C (C=0.19, Mn=0.7, Si 0.22, S=0.019, P=0.020: all are in wt.%) were prepared with a groove at one end for holding them in a salt bath furnace. The samples were first austenitised at 1000 °C for 15 min and then rapidly transferred to a salt bath kept at 670 ± 5 °C. Samples were immersed in the bath for different durations
Results and discussion
Initial results have been obtained, using this model, on transformation kinetics and pictorial views of microstructural evolution. The isothermal transformation kinetics of austenite to ferrite transformation at 670 °C for this low carbon steel has been determined with the help of the two-dimensional CA model as well as experimentally. The experimental points along with the model simulated results for fraction transformed are plotted against time as shown in Fig. 3. It is clear from the figure
Conclusion
- 1.
It has been shown that CA modelling technique can be successfully used for phase transformation modelling, with some unique features which are absent in conventional modelling techniques.
- 2.
In this modelling method the issues of ‘soft impingement’ and ‘hard impingement’ are taken care of elegantly.
- 3.
A complete picture of microstructural evolution can be obtained by using this modelling approach, which is a unique feature of CA modelling.
- 4.
CA modelling technique is probably the only one in which
Acknowledgements
We would like to thank Prof. H.K.D.H. Bhadeshia of Cambridge University, UK, for clarifying many doubts about the nucleation and diffusion model. We are also grateful to Dr. R. Sasikumar and Dr. M. Verma of RRL Trivandam, India, for introducing us to the subject of CA modelling.
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