# A coupled finite element-cellular automaton model for the prediction of dendritic grain structures in solidification processes

## Abstract

A new algorithm based upon a 2-dimensional Cellular Automaton (CA) technique is proposed for the simulation of dendritic grain formation during solidification. The CA model takes into account the heterogeneous nucleation, the growth kinetics and the preferential growth directions of the dendrites. This new CA algorithm, which applies to non-uniform temperature situations, is fully coupled to an enthalpy-based Finite Element (FE) heat flow calculation. At each time-step, the temperature at the cell locations is interpolated from those at the FE nodal points in order to calculate the nucleation-growth of grains. The latent heat released by the cells and calculated using a Scheil-type approximation is fed back into the FE nodal points. the coupled CA-FE model is applied to two solidification experiments, the Bridgman growth of an organic alloy and the one-dimensional solidification of an Al-7wt% Si alloy. In the first case, the predicted boundaries between grains are in good agreement with experiment, providing the CA cell size is of the order of the dendrite spacing. For the second experiment, the quality of the coupled CA-FE model is assessed based upon grain structures and cooling curves. The columnar-to-equiaxed transition and the occurrence of a recalescence are shown to be in goodmore »

- Authors:

- (Ecole Polytechnique Federale, Lausanne (Switzerland). Lab. de Metallurgie Physique)

- Publication Date:

- OSTI Identifier:
- 7278658

- Resource Type:
- Journal Article

- Journal Name:
- Acta Metallurgica et Materialia; (United States)

- Additional Journal Information:
- Journal Volume: 42:7; Journal ID: ISSN 0956-7151

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; ALUMINIUM ALLOYS; SOLIDIFICATION; DENDRITES; GRAIN GROWTH; SILICON ALLOYS; BRIDGMAN METHOD; COMPUTERIZED SIMULATION; CRYSTAL GROWTH; MATHEMATICAL MODELS; THEORETICAL DATA; ALLOYS; CRYSTAL GROWTH METHODS; CRYSTALS; DATA; INFORMATION; NUMERICAL DATA; PHASE TRANSFORMATIONS; SIMULATION; 360101* - Metals & Alloys- Preparation & Fabrication; 360102 - Metals & Alloys- Structure & Phase Studies

### Citation Formats

```
Gandin, C.A., and Rappaz, M.
```*A coupled finite element-cellular automaton model for the prediction of dendritic grain structures in solidification processes*. United States: N. p., 1994.
Web. doi:10.1016/0956-7151(94)90302-6.

```
Gandin, C.A., & Rappaz, M.
```*A coupled finite element-cellular automaton model for the prediction of dendritic grain structures in solidification processes*. United States. doi:10.1016/0956-7151(94)90302-6.

```
Gandin, C.A., and Rappaz, M. Fri .
"A coupled finite element-cellular automaton model for the prediction of dendritic grain structures in solidification processes". United States. doi:10.1016/0956-7151(94)90302-6.
```

```
@article{osti_7278658,
```

title = {A coupled finite element-cellular automaton model for the prediction of dendritic grain structures in solidification processes},

author = {Gandin, C.A. and Rappaz, M.},

abstractNote = {A new algorithm based upon a 2-dimensional Cellular Automaton (CA) technique is proposed for the simulation of dendritic grain formation during solidification. The CA model takes into account the heterogeneous nucleation, the growth kinetics and the preferential growth directions of the dendrites. This new CA algorithm, which applies to non-uniform temperature situations, is fully coupled to an enthalpy-based Finite Element (FE) heat flow calculation. At each time-step, the temperature at the cell locations is interpolated from those at the FE nodal points in order to calculate the nucleation-growth of grains. The latent heat released by the cells and calculated using a Scheil-type approximation is fed back into the FE nodal points. the coupled CA-FE model is applied to two solidification experiments, the Bridgman growth of an organic alloy and the one-dimensional solidification of an Al-7wt% Si alloy. In the first case, the predicted boundaries between grains are in good agreement with experiment, providing the CA cell size is of the order of the dendrite spacing. For the second experiment, the quality of the coupled CA-FE model is assessed based upon grain structures and cooling curves. The columnar-to-equiaxed transition and the occurrence of a recalescence are shown to be in good agreement with the model.},

doi = {10.1016/0956-7151(94)90302-6},

journal = {Acta Metallurgica et Materialia; (United States)},

issn = {0956-7151},

number = ,

volume = 42:7,

place = {United States},

year = {1994},

month = {7}

}