Convective coarsening of secondary dendrite arms

Abstract

Coarsening of secondary dendrite arms in binary and multi-component alloys has been investigated theoretically and experimentally since decades and it generally is accepted that the secondary arms coarsen as the cube root of solidification time. Recent experimental investigation with AlSi, AlSiMg and AlSiCu alloys using gentle magnetic stirring in directional solidification experiments show that the coarsening kinetics are changed. Instead of a cube root relation it is observed that the secondary arms coarsen as the square root of solidification time. This paper describes a theoretical model for the secondary arm spacing based on an Ostwald ripening model with convective mass transport. The model predicts a coarsening in accordance with the experiments and correctly predicts increasing stirring magnitude accelerates coarsening. It also makes predictions on the effect of the permeability of the mush on the coarsening rate factor.