Predicting freckle-defects in directionally solidified Pb-Sn alloys

This work validates a finite element model of dendritic solidification by comparing predicted results to data resulting from 11 directionally solidified hypoeutectic Pb-Sn samples, which were produced under various thermal gradients and solidification growth rates. For all but one of the cases, which was thought to be borderline between freckling and not freckling, predictions of whether freckles formed were supported by experiments. It was also determined that freckling could be predicted by running a simulation with convection turned on only after a mushy zone was fully developed; this saves computational time and lends credibility to the notion of using a non-dimensional freckling criterion such as a Rayleigh number. Finally, with D as the diffusivity of Sn in the liquid and V the growth rate, setting the mesh spacing in the growth direction at only D/V at the dendrite tips, and allowing the element size to be coarser throughout the rest of the domain, the simulations accurately predicted freckling consistent with results produced using a uniform mesh spacing of D/V. By testing the simulated system to see whether convection produces freckles after a completely developed mushy zone evolves and by employing a non-uniform mesh, a considerable saving in computational time for predicting freckles was achieved.