Simulation of solidification grain structures with a multiple diffusion length scales model

Abstract : A cellular automaton (CA) - finite element (FE) model is presented for the prediction of micro-and macrosegregation based on solute diffusion. On the one hand an open microsegregation model is implemented. It applies to each solidifying CA cell, i.e. a representative elementary volume of the mushy zone. Diffusion in the solid and in the extradendritic liquid are modeled with analytical expressions for two length scales based on the primary and secondary dendrite arm spacing and assuming cylindrical geometries representative of the dendritic network. On the other hand an unstructured and anisotropic FE mesh adaptation is used. The FE mesh is generated based on an error estimation method of the average composition field. Mesh refinement takes place in regions located ahead of the mushy zone growth front where diffusion layers are built up due to segregation. As a result, the diffusion length scale outside the envelopes of mushy zones (i.e., in the intergranular liquid that surrounds the envelopes of the grains) is directly captured. Numerical implementations of the coupling between the CA and FE methods being validated by comparison with the predictions of other models, simulations are compared with experimental results in Al-Cu alloys; thus demonstrating the capability of the model to predict segregation based on the coupling between several length scales.