Multi-scale modeling of equiaxed dendritic solidification of Al-Cu at constant cooling rate

To provide quantitative predictions, multiscale models of dendritic solidification (e.g., GEM, DNN, CAFE) need to be validated and require model parameters, which can be calculated by phase-field simulations. We report on a multiscale modeling of dendritic solidification in samples that are cooled homogeneously at a constant rate. We consider three Al-Cu alloys and samples from thin to bulk thickness. We investigate how the alloy composition, the distance between the equiaxed dendrites and the sample thickness influence the transient growth velocity of the primary tips. Using 3D phase-field simulations, we calculate the tip selection parameter based on the microsolvability theory. We show that the selection parameter depends principally on the ratio between the sample thickness and the smallest tip diffusion length during the transient growth (D/v_m, where v_m is the maximum tip velocity). The extracted tip selection parameters are then used as inputs for three-dimensional grain envelope model (GEM) simulations. The comparison between TIPF and GEM shows that the GEM can reproduce transient growth of interacting equiaxed dendrites during cooling and can account for sample confinement effects.