Spheroidal particle stability in semisolid processing
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RODUCTION
THE desired starting material for semisolid forming is a partially solidified (or partially melted) alloy in which the solid is present as nearly perfect spheroidal solid particles. Typically, the spheroidal structure, or something approaching it, is obtained by agitation during the initial dendrite formation as the alloy is cooled through the liquidus. The agitation ‘‘breaks’’ the fragile dendrites, creating multiple new grains, and therefore a fine grain structure. In the usual case in practice today, the grains then grow dendritically, but will ‘‘ripen’’ into spheroids of greater or lesser perfection on slow cooling, holding in the liquid-solid region or solidifying and reheating into the liquid-solid region. It is now understood that if initial grain density is sufficiently high, growth can be perfectly spheroidal throughout the growth process, obviating the need for ripening of a dendritic structure. A concomitant advantage is that spheroids obtained in this way have none of the entrapped second phase present in most ripened dendrites.[1,2] From a practical point of view in semisolid forming, the important basic issue is understanding the conditions of grain density, fraction solid, and cooling rate that permit solidification in a fully nondendritic, spheroidal mode. This work outlines those conditions, specifically comprising a modeling and experimental study of stability of the spheroidal particle interface in semisolid Al-4.5 wt pct Cu alloy as a function of solid fraction and cooling rate.
referred to as the ‘‘liquid diffusion controlled’’ (LDC) model. It assumes growth of a spherical particle of radius R, located at the center of a spherical volume of radius RT. The value of RT represents the radius of a sphere that would occupy the same volume as will the fully solidified grain. Thus, overall solute contained within the volume element of radius RT is conserved, and the model permits determining the effect of solute field overlap on the particle growth velocity. Figure 1 shows the model schematically, illustrating the solute profile in liquid and solid, at a time when solute diffusion fields have overlapped, so that the liquid concentration at R 5 RT is above the initial liquid concentration, C0/k. The following system of equations comprises the mathematical model: @C 1 @C @2C [1] 5 DL 1 2 @t r @r @r
dr @C C0 ð1 kÞ 5 DL dt @r r5R
[2]
ðTL TÞ 2G 1 1 mL mL R
[3]
CL C0 5
A. Growth Model, Numerical Solution A spherical particle growth model was developed for the semisolid Al-4.5 wt pct Cu alloy. The model assumes equilibrium at the spherical solid-liquid interface and no solid diffusion; the local solidification velocity is limited by solute diffusion away from the interface. The model is hereafter R.A. MARTINEZ, Process Engineering Manager, is with Selmet, Inc., Albany, OR 97321. Contact e-mail: [email protected] A. KARMA, Professor, is with the Physics Department, Northeastern University, Boston, MA 02115. M.C. FLEMINGS, Professor Emeritus, is with the Department of Materials Scienc
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