Modeling Micro Scale Phenomena for Application in Solidification Process Simulations

"Over the last ten years an increasing number of heat and mass transfer models of solidification processes have been presented in the literature. A key component in these models is the coupling between thermal and solute fields. This is achieved by developing relationships based on the behavior at the microscopic scale in the casting (typically a secondary dendrite arm space). An important class of models in this respect are models that describe the local scale redistribution of solute alloy components-collectively referred to as microsegregation models. This paper explores this class of models.IntroductionModeling takes a key role in processing materials for properties. This is particularly time in solidification processes where current computer techniques allow for a detailed treatment of the critical macroscopic phenomena. Typically these macro scale models consist ·of three main coupled components.1. A model of flow in the melt and solid + liquid mushy region.2. A model of heat transfer.3. A model of solute transport.The focus of this paper is the solute transport component, in particular the manner in which process scale transport is coupled to transport ·at the local scale of the solid-liquid interface. This step requires a modeling of the redistribution of solutes at the scale of the secondary arm spaces in the dendritic mushy region-a process referred to as microsegregation. Basic microsegregation models use the limit assumptions of no mass diffusion in the solid (Gulliver-Scheil [l]) or complete diffusion in the solid (equilibrium lever rule) in a fixed and space. Recently, however, more sophisticated microsegregation models that account for finite mass diffusion and coarsening of the arm space have been developed [2-19]. In this paper governing equations for a general microsegregation model for a multi-component alloy in a coarsening and spacing _are introduced. From these general equations various models for a binary system are developed and tested"