Abstract
A cellular automaton (CA) model to predict the formation of grain macrostructure during solidification has been implemented and the coupling between the microscopic and the macroscopic submodels has been investigated. The microscopic submodel simulates the nucleation and growth of grains, whereas the macroscopic solves the heat conduction equation. The directional solidification of an Al-7 wt. (%) Si alloy was simulated, enabling the calculation of the temperature and solid fraction profiles. The calculated temperature was used to obtain the solid fraction profile by an application of Scheil equation. This solid fraction disagrees with that calculated in the micro-macro coupling of the model, although this coupling is completely based on Scheil equation. Careful examination of the discrepancies shows that it is a result of the undercoolings for nucleation and growth of grains and also of the interpolations of enthalpy change and temperature from the finite volume mesh to the CA cell mesh.
Highlights
The cellular automaton (CA) technique is an algorithm constructed to simulate the spatial/temporal evolution of a system by applying simple transformation rules to the sites of a lattice[1], which is a set of fixed points
In the CA algorithm, provided the state values of all lattice points are known at the beginning of the simulation, the time evolution of these values is calculated after each time step using transformation rules based on the state of a lattice and its neighbors and, sometimes, on parameters such as temperature and concentration, depending on the type of model
Es in the mushy zone, down to TE; and (3) es < 1 below TE, solidification should end at TE
Summary
The cellular automaton (CA) technique is an algorithm constructed to simulate the spatial/temporal evolution of a system by applying simple transformation rules to the sites of a lattice[1], which is a set of fixed points. In the CA algorithm, provided the state values of all lattice points are known at the beginning of the simulation, the time evolution of these values is calculated after each time step using transformation rules based on the state of a lattice and its neighbors and, sometimes, on parameters such as temperature and concentration, depending on the type of model. Gandin and Rappaz[4] proposed one of the first models of solidification based on the CA technique This model evolved into the popular CAFE (cellular automaton - finite element) model[5], which was applied to predict grain macrostructures of alloys in the as-cast state[6].
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