Upscaling mesoscopic simulation results to develop constitutive relations for macroscopic modeling of equiaxed dendritic solidification

Abstract

Macroscale solidification models incorporate the microscale and mesoscale phenomena of dendritic grain growth using constitutive relations. These relations can be obtained by simulating those phenomena inside a Representative Elementary Volume (REV) and then upscaling the results to the macroscale. In the present study, a previously developed mesoscopic envelope model is used to perform three-dimensional simulations of equiaxed dendritic growth at a spatial scale that corresponds to a REV. The mesoscopic results are upscaled by averaging them over the mesoscopic simulation domain. The upscaled results are used to develop new constitutive relations, which, unlike the currently available relations, do not rely on highly simplified assumptions about the grain envelope shape or the solute diffusion conditions around it. The relations are verified by comparing the predictions of the macroscopic model with the upscaled mesoscopic results at different solidification conditions. These relations can now be used in macroscopic models of equiaxed solidification to incorporate more realistically the microscale and mesoscale phenomena.