Centerline porosity in plate castings
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I.
INTRODUCTION
A number of models have been developed which enable the position of centerline porosity in horizontal plate castings to be determined. The model developed by Davies ~ is primarily based on the ability of liquid to flow into the shrinkage cavities during solidification. A capillary feeding distance was calculated, based both on Darcy's Law and estimates of the liquid fraction present when capillary flow occurred. When the calculated results were compared with experimental data, an empirical correction factor was required to fit the calculated values to the experimental results. Assumptions were also required in the model for the fraction solid above which incomplete feeding could occur, which significantly affected the calculated feeding distance. Centerline porosity was also modeled by Flemings, 2 using Darcy's Law for determining the interdendritic fluid flow, and heat flow analysis to determine the liquid fraction present when flow occurred. The analysis developed an expression for the pressure at a given point in the casting required to fill the shrinkage porosity. In the heat transfer analysis it was assumed that heat flux was primarily controlled by the mold/metal interface; the heat entering the mold came entirely from the heat of fusion of the solidifying metal; and that there was no significant thermal gradient in the solidifying metal. These assumptions are generally not valid for cast plates. In the present investigation explicit finite difference solutions of the heat flow equations were used to calculate the position of the solidus and liquidus in the casting during solidification. From the position of the solidus and liquidus, the fraction solid at any point could be determined without the assumptions concerning heat flow used by Flemings. These results coupled with capillary fluid flow based on Darcy's Law, and permeability data, enabled local pressures to be calculated which were required to fill shrinkage porosity. The calculated local pressures were then compared to the actual pressures throughout the system. If the actual pressure at a given point was less than the pressure required to fill the shrinkage, then porosity would occur.
green sand or a chill at the other as shown in Figure 1. The thickness of the plate is s and the length I varies between 4s and 12s. Centerline shrinkage has been observed to occur in the region indicated. 3
A. Metal Temperatures during Solidification The temperature distribution in the system can be calculated from the general heat conduction equation:
St
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~
PROCEDURE
The model considers the solidification of a horizontal steel plate cast in green sand with a riser at one end and S. MINAKAWA, Engineer, is with Riken Corporauon, Tokyo, Japan. I. V. SAMARASEKERA, Assistant Professor, and F WEINBERG, Professor, are with the Department of Metallurgical Engmeenng, University of British Columbia, Vancouver, BC V6T 1W5, Canada Manuscript submxtted January 28, 1985 METALLURGICALTRANSACTIONS B
+
Oy-/
[1]
assuming constant thermal conductivity and t
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