Solidification of metal spheres
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ALUMINUM L-S INTERFACE --DURING MELTING ------DURING SOLIDIFICATION TOP HAT LASERBEAM TEMPERATURE DEPENDENT ABSORPTIVITY qa =
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Fig. 2--Liquid-solid interface during melting and subsequent solidification of an aluminum substrate subjected to a top hat laser beam with temperature dependent absorptivity. The curve marked T(0,0) = T v shows location of interface at the time the heat flux was removed. *Note: The z/a scale is twice that of r/a scale.
pected because of the fact that surface absorption increases with increasing temperature. Figure 2 shows the liquid-solid interface during melting and subsequent solidification of an aluminum substrate with temperature dependent surface absorptivity subjected to an uniform (top hat) laser beam. The
Solidification of Metal Spheres JOHN M. FORGAC AND JOHN C. ANGUS In the absence of other forces, surface tension will cause liquid metal drops to assume a spherical shape. If solidified, these droplets of liquid metal can remain intact, producing spheres, or they can rupture, producing irregular shapes. A recent analysist of stresses developed during solidification of a sphere permits identification of the factors which lead to these very different outcomes. The thermoelastic modeP predicts very large internal negative pressures in the liquid core as solidification nears completion. We examine three possible outcomes as the internal negative pressure and stresses in the solid shell increase: 1) buckling of the solid shell, 2) cavity formation in the liquid core, and 3) plastic deformation of the solid shell. In order to form a solid sphere it is necessary that the thin solid shell present during the early stages of solidification not buckle or deform. The modeP shows JOHN M. FORGAC is Research Engineer, Amoco Oil Company, P.O. Box 400, Naperville, IL 60566, and JOHN C. ANGUS is Professor of Engineering, Department of Chemical Engineering, Case Western Reserve University, Cleveland, OH 44106. Manuscript submitted July 2, 1979. METALLURGICAL TRANSACTIONS B
beam was turned off when the center of the spot reached the vaporization temperature. The absorptivity values used here are relatively low due to the very clean and polished surfaces of the specimens on which they were measured. In commercial practice, surface roughness and oxidation result in significantly higher values. However, the general trends relating constant to variable absorptivity established here should be equally applicable. Finally, it should be mentioned that the form of variable absorptivity used for this paper is valid only prior to any plasma formation or evaporation.
1. M.I. Cohen: J. Franklin Inst., 1967, vol. 283, p. 271. 2. S.C. Hsu, S. Chakravorty, and R. Mehrabian: Metall. Trans. B., 1978, vol. 9B, p.221. 3. S.C. Hsu, S. Kou, and R. Mehrabian: Metall. Trans. B., 1980, vol. 11B, p.29. 4. D.
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