The occurrence of ripples on the workpiece surface after solidification in electron-beam welding or melting is experimentally and analytically investigated. The maximum accelerating voltage and welding current of the electron-beam welder are 60 kV and 50 mA, respectively, while the workpieces are Al 1100 and SS 304. The average pitches and amplitudes of surface ripples are measured for different beam powers and welding speeds. Using a scale analysis to account for heat transfer and fluid flow induced by a negative temperature-dependent surface tension gradient in the molten pool the variations of ripples with dimensionless beam power, Marangoni, Peclet, Prandtl, Stefan, and Biot numbers are found for the first time. The predicted results show good agreement with experimental data.

1.
Anthony
T. R.
, and
Cline
H. E.
,
1977
, “
Surface Rippling Induced by Surface-Tension Gradien ts During Laser Surface Melting and Alloying
,”
Journal of Applied Physics
, Vol.
48
, pp.
3888
3894
.
2.
Arata
Y.
,
Matsuda
F.
, and
Murakami
T.
,
1973
, “
Some Dynamic Aspects of Weld Molten Metal in Electron Beam Welding
,”
Transactions of Japan Welding Research Institute
, Vol.
2
, pp.
23
32
.
3.
Bejan, A., 1984, Convective Heat Transfer, Wiley, New York, Chap. 2.
4.
Burgardt, P., 1986, “Electron Beam Beam Size Calibration,” Summary of Calibration of Welding Systems Meeting, L. N. Tallerico, ed., Sandia National Lab., Livermore, CA, Feb., pp. 258–266.
5.
Christensen
N.
,
Davies
V. de L.
, and
Gjermundsen
K.
,
1965
, “
Distribution of Temperatures in Arc Welding
,”
British Welding Journal
, Vol.
12
, pp.
54
75
.
6.
D’annessa
A. T.
,
1970
, “
Sources and Effects of Growth Rate Fluctuations During Weld Metal Solidification
,”
Welding Journal
, Vol.
49
, pp.
41-s–45-s
41-s–45-s
.
7.
Eagar
T. W.
, and
Tsai
N.-S.
,
1983
, “
Temperature Fields Produced by Traveling Distributed Heat Sources
,”
Welding Journal
, Vol.
62
, pp.
346-s to 355-s
346-s to 355-s
.
8.
Ecer, G. M., Tzavaras, A., Gokhale, A., and Brody, H. D., 1982, “Weld Pool Fluid Motion and Ripple Formation in Pulsed-Current GTAW,” in: Trends in Welding Research in the United States, S. A. David, ed., Proceedings of a conference sponsored by the Joining Division of American Society for Metals, New Orleans, Nov. 16-18, 1981, pp. 419–442.
9.
Garland
J. G.
, and
Davies
G. J.
,
1970
, “
Surface Rippling and Growth Perturbations During Weld Pool Solidification
,”
Metal Construction and British Welding Journal
, Vol.
2
, pp.
171
175
.
10.
Giedt
W. H.
, and
Tallerico
L. N.
,
1988
, “
Prediction of Electron Beam Depth of Penetration
,”
Welding Journal
, Vol.
67
, pp.
299-s to 305-s
299-s to 305-s
.
11.
Hicken
G. K.
,
Giedt
W. H.
, and
Bentley
A. E.
,
1991
, “
Correlation of Joint Penetration With Electron Beam Current Distribution
,”
Welding Journal
, Vol.
70
, pp.
69-s-75-s
69-s-75-s
.
12.
Kamotani
Y.
,
Ostrach
S.
, and
Pline
A.
,
1995
, “
A Thermocapillary Convection Experiment in Microgravity
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
117
, pp.
611
618
.
13.
Mills
K. C.
, and
Keene
B. J.
,
1990
, “
Factors Affecting Variable Weld Penetration
,”
International Materials Reviews
, Vol.
35
, pp.
185
216
.
14.
O’Brien, R. L., ed., 1991, Welding Handbook, Welding Processes, Vol. 2, 8th ed., American Welding Society, Miami, p. 64.
15.
Ostrach
S.
,
1982
, “
Low-Gravity Fluid Flows
,”
Annual Reviews of Fluid Mechanics
, Vol.
14
, pp.
313
345
.
16.
Ostrach
S.
,
Kamotani
Y.
, and
Lai
C. L.
,
1985
, “
Oscillatory Thermocapillary Flows
,”
PCH PhysicoChemical Hydrodynamics
, Vol.
6
, pp.
585
599
.
17.
Rivas
D.
, and
Ostrach
S.
,
1992
, “
Scaling of Low-Prandtl-number Thermocapillary Flows
,”
International Journal of Heat and Mass Transfer
, Vol.
35
, pp.
1469
1479
.
18.
Rivas
D.
,
1991
, “
High-Reynolds-Number Thermocapillary Flows in Shallow Enclosures
,”
Physics of Fluids A
, Vol.
3
, pp.
280
291
.
19.
Rosenthal
D.
,
1941
, “
Mathematical Theory of Heat Distribution During Welding and Cutting
,”
Welding Journal
, Vol.
20
, pp.
220-s to 234-s
220-s to 234-s
.
20.
Schwabe
D.
, and
Scharmann
A.
,
1979
, “
Some Evidence for the Existence and Magnitude of a Critical Marangoni Number for the Onset of Oscillatory Flow in Crystal Growth Melts
,”
Journal of Crystal Growth
, Vol.
46
, pp.
125
131
.
21.
Sen
A. K.
, and
Davis
S. H.
,
1982
, “
Steady Thermocapillary Flows in Two-Dimensional Slots
,”
Journal of Fluid Mechanics
, Vol.
121
, pp.
163
186
.
22.
Strani
M.
,
Piva
R.
, and
Graziani
G.
,
1983
, “
Thermocapillary Convection in a Rectangular Cavity: Asymptotic Theory and Numerical Simulation
,”
Journal of Fluid Mechanics
, Vol.
130
, pp.
347
376
.
23.
Tong
H.
, and
Giedt
W. H.
,
1969
, “
Radiographs of the Electron Beam Welding Cavity
,”
The Review of Scientific Instruments
, Vol.
40
, pp.
1283
1285
.
24.
Wei
P. S.
, and
Chow
Y. T.
,
1992
, “
Beam Focusing Characteristics and Alloying Element Effects on High-Intensity Electron Beam Welding
,”
Metallurgical Transactions B
, Vol.
23B
, pp.
81
90
.
25.
Wei
P. S.
, and
Shian
M. D.
,
1993
, “
Three-Dimensional Analytical Temperature Field Around the Welding Cavity Produced by a Moving Distributed High-Intensity Beam
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
115
, pp.
848
856
.
26.
White, F. M., 1979, Fluid Mechanics, McGraw-Hill, New York, pp. 353–360.
27.
Xu
J-J.
, and
Davis
S. H.
,
1984
, “
Convective Thermocapillary Instabilities in Liquid Bridges
,”
Physics of Fluids
, Vol.
27
, pp.
1102
1107
.
28.
Zebib
A.
,
Homsy
G. M.
, and
Meiburg
E.
,
1985
, “
High Marangoni Number Convection in a Square Cavity
,”
Physics of Fluids
, Vol.
28
, pp.
3467
3476
.
This content is only available via PDF.
You do not currently have access to this content.