A numerical study of thermal interaction of solidification fronts with spherical particles during solidification of metal-matrix composite materials

Abstract

The potential influence of the presence of copper, iron, mica, TiB 2, graphite and alumina particles dispersed in melts of several matrix metals including aluminum, copper and lead was studied. Specifically the influence of the particles on the solidification fronts during freezing of various matrix melts was numerically studied in order to understand the experimentally observed solidification microsctructures in metal-matrix composites. Irregular geometries of the composite material were mapped into simple rectangles through numerical conformal mapping techniques to analyse the influence of a single particle or a row of particles on a unidirectionally advancing planar solidification front. The particles were assumed to be spherical and located in the center of the cylindrical mold. The study showed that for particles with lower thermal conductivity than the melt, the interface first goes through acceleration as it approaches and encapsulates the front half of the particle, and then it decelerates as it encapsulates the remaining half of the particle. The acceleration and deceleration phenomenon of the interface increases as the thermal conductivity ratio of particle to melt decreases. With low thermal conductivity ratios ( K p K l ⪡ 1 ), the interface is orthogonal to the particle. When the conductivity of the particle is lower than that of the melt, the interface becomes convex facing the particle; this mode would lead to pushing of the particle ahead if it was free to move as has been experimentally observed during solidification of several metal-matrix composites when K p K l ⪢ 1 , the phenomenon is the opposite to that mentioned above and the interface would become concave facing the particle tending to entrap the particle. The temperature vs solidification time plots of two points, one in the particle and the other in melt, show that the particle with a conductivity lower than the matrix is at a temperature higher than the melt; the temperature difference between the two points decreases with increasing solidification rate for all the positions of the interface before it touches the particle. The influences of these temperature differences between the melt and the particles on solidification of composites are discussed.