On the calculation of the free surface temperature of gas-tungsten-arc weld pools from first principles: Part I. modelin
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I.
INTRODUCTION
THE purpose of this article is to report on recent research results that enable us to predict with some confidence the temperature profiles that exist on the free surface of weld pools. This article consists of two parts: in Part 1, the arc model development and results will be given, while in Part II, t34] the weld pool will be addressed. Figure 1 shows a schematic sketch of a gas tungsten arc welding (GTAW) operation, where it is seen that a plasma arc is made to impinge on the free surface of the weld pool; this plasma arc provides the energy needed to melt the weld metal. In recent years, major research efforts have been focused on the study of the behavior of both weld pools ~1-51 and arcs, ~6-8.12-141 but the precise way the weld pool and the arc interact has been much less well explored. More specifically, in most previous publications, the effect of the arc or of the heat source, in general, has been introduced as a "boundary condition" which could be specified essentially independently of the weld pool behavior. In a recent article, the present authors I6~ have shown that such an assumption is an oversimplification in the majority of cases; indeed, the two-way interaction between the weld pool and the plasma arc was shown to be a highly desirable feature of weld pool modeling efforts. The present article represents an extension and quantification of these ideas, with emphasis on the prediction of the free surface temperature of the weld pool. Figure 2 shows a schematic sketch of the weld pool in a spot welding operation. It is seen that the circulation in the weld pool may be affected by four distinct driving forces, namely, (1) surface tension gradients, (2) gas drag, R.T.C. CHOO, Research Associate, is with the Department of Metallurgy and Materials Science, University of Toronto, Toronto, ON M5S 1A4, Canada. J. S Z E K E L Y , P r o f e s s o r , and R.C. WESTHOFF, Graduate Student, are with the Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139. Manuscript submitted June 10, 1991. METALLURGICAL TRANSACTIONS B
(3) electromagnetic forces, and (4) buoyancy. Previous studies have shown that surface tension gradients, which in turn are generated by temperature gradients, often represent the dominant driving force for weld pool motion. While surface tension gradients may also be affected by such variables as the weld pool shape and the composition of the workpiece, it is evident that the precise knowledge of the free surface temperature profile is essential for the proper representation of this effect. There is one even more important reason why one needs to know the temperature at the free surface, which is associated with determining the net heat flow to the weld pool. This net heat flow is governed by the balance between the energy received from the welding arc (due to the combination of electronic, convective, and radiative heat fluxes) and the heat loss from the free surface due to vaporization. In order to assess this heat loss
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