A mathematical model of the planar flow melt spinning process
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I.
INTRODUCTION
D U R I N G the past two decades a great deal of interest has been developed in rapid solidification as a means for producing glassy or microcrystalline substances of attractive mechanical, magnetic, and corrosion resistant properties. This technology is now well documented. 1,2,3It is fair to say that in the study of the various rapid solidification technology (RST) applications, most of the attention has been centered on the characterization and evaluation of the materials produced, while the investigations into the actual processing fundamentals have been rather smaller in number. Of the numerous RST operations currently in use, the melt spinning processes are, perhaps, the most commonly employed. A common feature of all these operations is that a metal stream is brought into contact with a cooled rotating wheel and as a result a thin, rapidly solidified ribbon is being produced. As illustrated in Figure 1, there are two basic variants of this technology, namely the chill block process (CBP), and the planar flow process (PFP). In the CBP the nozzle, supplying the molten feed, is placed at a distance from the wheel, whereas in the PFP the nozzle is brought into the close proximity of the quenching wheel. In this latter mode of operation the molten puddle is constrained between the moving wheel and the lip of the nozzle which is thought to enhance the stability of the process and allow for a better control of the final ribbon width and thickness. The purpose of the present paper is to develop a fundamentally based quantitative representation of the heat and fluid flow phenomena in the PFP, with the ultimate objective of relating the key process parameters, such as the ribbon thickness, the solidification rate, and the microstructure to the geometry of the system and the operating conditions. While useful prior modeling work has been published in the literature, 4-~~ the entirety of the problem, as described above, has yet to be tackled. More specifically, the previous investigators employed somewhat simplified fluid and heat flow considerations and have neglected the free surface (meniscus) aspect of the problem. Nor has their analysis accounted for melt recirculation. Finally, virtually all the previous work has concentrated on modeling the formation of metallic glasses. The liberation of the latent heat of E.M. GUTIERREZ, Postdoctoral Research Associate, and J. SZEKELY, Professor of Materials Engineering, are with Massachusetts Institute of Technology, Department of Materials Science and Engineering. Cambndge. MA 02139. Manuscript submitted January 22. 1986. METALLURGICALTRANSACTIONS B
solidification, which is an inherent feature of the solidification of microcrystalline materials, has, therefore, not been taken into consideration.
II.
FORMULATION
Figure 2 shows a still frame from a high speed movie taken during the PF casting of a nickel based superalloy. The photo shows the wheel, the nozzle, and the melt puddle in between. The wheel is at the bottom and moves from left to right. The nozz
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