Three-dimensional convection in laser melted pools
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tension gradient at the pool surface. Laser surface melting of 6063 aluminum alloy was carried out using a continuous-wave CO: laser, and the power delivered to the workpiece was measured calorimetrically. The calculated and observed fusion boundaries were compared and very good agreement was obtained. Finally, the effect of the surface tension temperature coefficient O y / O T on the convection pattern and penetration of laser melted pools was demonstrated with the model.
I.
INTRODUCTION
T w o - d i m e n s i o n a l convection in stationary pools has recently been calculated by Oreper et al. ,~'2 Chan et al: ,3 and Kou et al. 4 The heat source was considered circular and Gaussian in the studies of Oreper et al. and of Kou et a l . , which is typical for both arc welding and laser surface melting. It was, however, treated as rectangular and uniform in the study of Chan et al. The heat of fusion was also neglected. These models represent a significant improvement over Rosenthal's original workfl Unfortunately, the heat source has to be considered stationary. In the present study, the computer model previously developed by Kou et al. 4 for two-dimensional convection in stationary pools was extended so that three-dimensional convection in moving pools could be studied. Since both laser welding and laser surface melting involve a moving pool most of the time, the present model is much more useful than those previous ones developed for stationary pools. The heat source was again considered circular and Gaussian, even though it could be treated as rectangular and uniform without any difficulties at all. The present study is part of our current work on heat flow and solidification in aluminum welds. For this reason, 6063 aluminum alloy was chosen in the study.
Fig. l--Schematic sketch of laser surface melting.
where V = p = P = ~- = fl = g = T = To = H = k =
velocity mass density pressure shear stress volumetric thermal expansion coefficient gravitational acceleration 9 temperature reference temperature enthalpy per unit mass thermal conductivity
The boundary conditions are as follows:
II.
MATHEMATICAL MODEL
(i) Top surface (z = 0)
Figure 1 shows the interaction between a stationary laser beam and a workpiece which moves at a constant speed U in the x-direction. The following equations describe the steady state velocity and temperature fields in the workpiece: v.
v
= 0
w=O Ou IX
- [ V . r] - p f i g ( T - To)
ix
[2]
k
(equation of motion) V " V ( p H - P) = V . (kVT)
[3]
(equation of energy)
Ox OT
Oz
Ov
[1]
(equation of continuity) p ( V " V)V = - V P
OT Oy -
OT Oz
OT Oy -
Oz
3Q
Oy OT
{-3r2~
- ~'a- e x p i - - ~ } '
forr_a
(ii) Bottom surface (z = g) u=U S. KOU, Professor, and Y.H. WANG, Graduate Student, are with the Department of Metallurgical and Mineral Engineering, University of Wisconsin, Madison, WI 53706. Manuscript submitted November l l, 1985. METALLURGICAL TRANSACTIONS A
v=w=O
_kO__T = h ( V Oz
~ro) + o - e ( T 4 -
T 4)
VOLUME 17A. DECEMBER 1986--2265
(iii) Center pla
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