Mushy zone modeling with microstructural coarsening kinetics

Abstract

A key element of mushy zone modeling is the description of the microscopic evolution of the lengthscales within the mushy zone and the influence of macroscopic transport processes. This article describes some recent progress in developing a mean-field statistical theory of phase coarsening in adiabatic mushy zones. The main theoretical results are (1) temporal scaling laws that indicate that the average lengthscale increases as time^1/3, (2) a self-similar distribution of mushy zone lengthscales based on spherical solid particle shapes, and (3) kinetic rate constants which provide the dependences of the coarsening process on material parameters and the volume fraction of the solid phase. High precision thermal decay experiments are described which verify aspects of the theory in pure material mushy zones held under adiabatic conditions. The microscopic coarsening theory is then integrated within a simple macroscopic heat-transfer model of one-dimensional alloy solidification. The method demonstrates an ability to predict the influence of macroscopic heat transfer on the evolution of primary and secondary dendrite arm spacings in Al-Cu alloys.