The thermal evolution of liquid and solid during the radially inward solidification of spherical balls of liquid has been studied by accounting for the increase in the density as phase transition occurs from liquid to solid. With this increase in density, the system geometry becomes that of a hollow sphere with a void at the center. We consider pure metals and binary alloys. For alloy solidification, the void begins to grow only after the outer surface reaches the solidus temperature. The temperature dependence of the thermophysical properties of the two phases is taken into account along with the natural convective and radiative loss to the ambient. The model has been applied to pure aluminum, Al – 1% Si, Al - 1% Mg, and Al - 2% Mg for a range of initial radii of the balls. From this study, we conclude that: (a) the volume fraction of the shrinkage void in the ball is independent of the initial radius for pure metal while it increases monotonically with initial radius for the binary alloys, and (b) for identical conditions, the voids are much smaller in alloys than in the pure metal.
An Analysis of Shrinkage Porosity in Aluminum Ball Bonding Process
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Huang, L. J., Ramakrishna, K., Ayyaswamy, P. S., and Cohen, I. M. (September 1, 1989). "An Analysis of Shrinkage Porosity in Aluminum Ball Bonding Process." ASME. J. Electron. Packag. September 1989; 111(3): 199–206. https://doi.org/10.1115/1.3226534
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