About the shape of eutectic grains solidifying in a thermal gradient

Abstract

In eutectic alloys solidified in a thermal gradient, it has been observed that the final shape of the grains nucleated in the bulk of the liquid is more elongated in the direction opposite to that of the heat flow. This experimental result appears to be in contradiction with that expected for the growth of an isolated grain, since the portion of the interface located in the downstream heat flow direction is the most undercooled and thus has the highest growth rate. However, when considering a family of grains which continuously nucleate in the bulk of the liquid, it is shown that the impingement of the grains limits their growth in the downstream heat flow direction and thus explains their final shape. In order to investigate this phenomenon, the differential equation which governs the growth of an isolated eutectic grain in a thermal gradient has been derived and solved analytically for the two extreme positions of the interface along the heat flow direction. Using these relationships, the asymmetry factor of the grains has been deduced as a function of the solidification parameters. The overall shape of an isolated grain has also been predicted using numerical integration. Finally, these results are integrated into a stochastic model of grain structure formation and the simulated microstructure is compared with experimental micrographs previously obtained for hypereutectic aluminium-silicon alloys remelted by laser.