Multiscale prediction of microstructure length scales in metallic alloy casting

In this article, we combine casting experiments and quantitative simulations to present a novel multiscale modeling approach to predict local primary dendritic spacings in metallic alloys solidified in conditions relevant to industrial casting processes. To this end, primary dendritic spacings were measured in instrumented casting experiments in Al-Cu alloys containing 1\,wt\% and 4\,wt\% of Cu, and they were compared to spacing stability ranges and average spacings in dendritic arrays simulated using phase-field (PF) and dendritic needle network (DNN) models. It is first shown that PF and DNN lead to similar results for the Al-1\,wt\%Cu alloy, using a dendrite tip selection constant calculated with PF in the DNN simulations. PF simulations cannot achieve quantitative predictions for the Al-4\,wt\%Cu alloy because they are too computationally demanding due to the large separation of scale between tip radius and diffusion length, a characteristic feature of non-dilute alloys. Nevertheless, the results of DNN simulations for non-dilute Al-Cu alloys are in overall good agreement with our experimental results as well as with those of an extensive literature review. Simulations consistently suggest a widening of the PDAS stability range with a decrease of the temperature gradient as the microstructure goes from cellular-dendrites to well-developed hierarchical dendrites.