Three-dimensional heat flow and solidification during the autogenous GTA welding of aluminum plates
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I.
INTRODUCTION
BOTHthe two-dimensional heat flow during the autogenous (i.e., without filler metal) GTA (i.e., gas tungsten arc) welding of thin sheets and the three-dimensional heat flow during the autogenous GTA welding of semi-infinite plates have been solved analytically. 1,2For simplicity, assumptions such as a point heat source and zero heat of fusion were made. The three-dimensional heat flow during the autogenous GTA welding of plates of finite thickness, however, has not been solved analytically so far. In fact, only recently have Friedman et al. 3'4 developed the first computer model which allows the calculation of heat flow during the autogenous GTA welding of plates of finite thickness. The finite element method was employed and heat conduction in the welding direction was neglected in their heat flow model. Since the model is two dimensional, it is not ideal for the purpose of solidification studies. In the present work, a three-dimensional heat flow model was developed based on the finite difference method, with heat conduction in the welding direction being considered. This model is applicable to plates of any thickness. It was used to study heat flow and solidification during the autogenous GTA welding of moderately thick aluminum plates. It should be pointed out that the three-dimensional heat flow model developed previously by one of the authors s is valid for semi-infinite plates only. Neither thin sheets nor moderately thick plates can be considered in such a model. II.
fully or partially penetrating, depending on the welding parameters used. Behind the molten pool is the weld fusion zone, which is often called the weld bead. The coordinate system (x-y-z) shown in the same figure moves with the heat source at the same velocity, and its origin coincides with the center of the heat source. Due to the combined effects of the electromagnetic force, the plasma jet force, and the surface tension of the liquid metal, the convection in the molten pool appears to be rather complex in arc welding. No attempts were made here to simulate the liquid pool convection. Rather, the effective thermal conductivity6'7's was used to account for the effect of such a liquid convection on heat flow during welding. The following integral energy equation was used to describe the energy balance in a volume element of the workpiece:
_
ffrll UO(PH)d~dydz dx
[1]
.UJ
where H is the enthalpy, p the density, t time, k the thermal conductivity, T temperature, and S the total surface area of the volume element. Except during the initial and the final transients of the welding process, the temperature distribution in a workpiece of sufficient length is steady with respect to a coordinate
MATHEMATICAL MODEL
Shown in Figure 1 is a schematic sketch of autogenous GTA welding. The heat source is moving at a constant velocity U. As a result of the heat input, a molten pool is created under the heat source. The weld pool can be either S. KOU, Associate Professor, and Y. LE, Graduate Student, formerly with the Department of Met
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