This paper presents a quasi-steady stagnation flow analysis for the material removal processes in high-intensity laser materials processing, such as laser drilling. The governing stagnation flow equations for the heat transfer and fluid flow phenomena are derived for the region near the centerline of the laser beam. The analysis accounts for conduction in the solid, conduction, and convection in the melt layer, and the latent heats of melting and vaporization. The stagnation flow governing equations and boundary conditions are appropriately normalized and solved, and the important combinations of material properties and independent laser parameters are identified. This semiquantitative analysis yields quasi-steady estimates for the penetration velocity, the thickness of the melt layer, the velocity and temperature profiles in the melt layer, and the fraction of melt that is vaporized for varying absorbed laser power and beam radius. Inviscid results from the stagnation flow analysis are shown for five different materials: aluminum, copper, low carbon steel, stainless steel, and titanium. Relatively good agreement exists between the results from the analysis and experimental data from the literature. [S0022-1481(00)01804-1]

1.
Minardi
,
A.
, and
Bishop
,
M. J.
,
1988
, “
Two-Dimensional Temperature Distribution Within a Metal Undergoing Multiple Phase Changes Caused by Laser Irradiation at the Surface
,”
ASME J. Heat Transfer
,
110
, pp.
1009
1011
.
2.
Armon
,
E.
,
Zvirin
,
Y.
,
Laufer
,
G.
, and
Solan
,
A.
,
1989
, “
Metal Drilling with a CO2 Laser Beam
,”
J. Appl. Phys.
,
65
, No.
12
, pp.
4995
5002
.
3.
Kar
,
A.
, and
Mazumder
,
J.
,
1990
, “
Two-Dimensional Model for Material Damage Due to Melting and Vaporization During Laser Irradiation
,”
J. Appl. Phys.
,
68
, No.
8
, pp.
3884
3891
.
4.
Wei
,
P. S.
, and
Ho
,
J. Y.
,
1990
, “
Energy Considerations in High-Energy Beam Drilling
,”
Int. J. Heat Mass Transf.
,
33
, No.
10
, pp.
2207
2217
.
5.
Armon
,
E.
,
Zvirin
,
Y.
, and
Solan
,
A.
,
1991
, “
Numerical Simulation of Metal Drilling with a CO2 Laser Beam
,”
Numer. Heat Transfer, Part B
,
19
, pp.
85
104
.
6.
Yilbas
,
B. S.
,
Sahin
,
A. Z.
, and
Davies
,
R.
,
1995
, “
Laser Heating Mechanism Including Evaporation Process Initiating Laser Drilling
,”
Int. J. Mach. Tools Manuf.
,
35
, No.
7
, pp.
1047
1062
.
7.
Modest
,
M. F.
,
1996
, “
Three-Dimensional, Transient Model for Laser Machining of Ablating/Decomposing Materials
,”
Int. J. Heat Mass Transf.
,
39
, No.
2
, pp.
221
234
.
8.
Modest
,
M. F.
,
1997
, “
Laser Through-Cutting and Drilling Models for Ablating/Decomposing Materials
,”
J. Laser Appl.
,
9
, pp.
137
145
.
9.
Yilbas
,
B. S.
, and
Al-Garni
,
A. Z.
,
1996
, “
Some Aspects of Laser Heating of Engineering Materials
,”
J. Laser Appl.
,
8
, pp.
197
204
.
10.
Yilbas
,
B. S.
,
1995
, “
Study of Liquid and Vapor Ejection Processes During Laser Drilling of Metals
,”
J. Laser Appl.
,
7
, pp.
145
152
.
11.
Yilbas
,
B. S.
, and
Sami
,
M.
,
1997
, “
Liquid Ejection and Possible Nucleate Boiling Mechanisms in Relation to the Laser Drilling Process
,”
J. Phys. D: Appl. Phys.
,
30
, pp.
1996
2005
.
12.
von Allmen
,
M.
,
1976
, “
Laser Drilling Velocity in Metals
,”
J. Appl. Phys.
,
47
, No.
12
, pp.
5460
5463
.
13.
Chan
,
C. L.
, and
Mazumder
,
J.
,
1987
, “
One-Dimensional Steady-State Model for Damage by Vaporization and Liquid Expulsion Due to Laser-Material Interaction
,”
J. Appl. Phys.
,
62
, No.
11
, pp.
4579
4586
.
14.
Wei
,
P. S.
, and
Chiou
,
L. R.
,
1988
, “
Molten Metal Flow Around the Base of a Cavity During a High-Energy Beam Penetrating Process
,”
ASME J. Heat Transfer
,
110
, pp.
918
923
.
15.
Kar
,
A.
,
Rockstroh
,
T.
, and
Mazumder
,
J.
,
1992
, “
Two-Dimensional Model for Laser-Induced Materials Damage: Effects of Assist Gas and Multiple Reflections Inside the Cavity
,”
J. Appl. Phys.
,
71
, No.
6
, pp.
2560
2569
.
16.
Ganesh
,
R. K.
,
Bowley
,
W. W.
,
Bellantone
,
R. R.
, and
Hahn
,
Y.
,
1996
, “
A Model for Laser Hole Drilling in Metals
,”
J. Comput. Phys.
,
125
, pp.
161
176
.
17.
Ganesh
,
R. K.
,
Faghri
,
A.
, and
Hahn
,
Y.
,
1997
, “
A Generalized Thermal Modeling for Laser Drilling Process—I. Mathematical Modeling and Numerical Methodolgy
,”
Int. J. Heat Mass Transf.
,
40
, No.
14
, pp.
3351
3360
.
18.
Ganesh
,
R. K.
,
Faghri
,
A.
, and
Hahn
,
Y.
,
1997
, “
A Generalized Thermal Modeling for Laser Drilling Process—II. Numerical Simulation and Results
,”
Int. J. Heat Mass Transf.
,
40
, No.
14
, pp.
3361
3373
.
19.
Semak
,
V. S.
, and
Matsunawa
,
A.
,
1997
, “
The Role of Recoil Pressure in Energy Balance During Laser Materials Processing
,”
J. Phys. D: Appl. Phys.
,
30
, pp.
2541
2552
.
20.
Chen
,
M. M
,
Bos
,
J. A.
, and
Batteh
,
J. J.
,
1997
, “
Parametric Study of Keyhole Behavior Based on an Approximate Theory
,”
Laser Institute of America, Proceedings
,
83
, No.
2
, pp.
G34–G43
G34–G43
.
21.
Bos, J. A., and Chen, M. M., 1998, “An Approximate Analysis of the Melt Flow and Heat Transfer in Deep Penetration Laser Welding,” presented at IMECE ’98.
22.
Schlichting, H., 1968, Boundary Layer Theory, 6th Ed., pp. 91–92.
23.
Mohanty
,
P. S.
,
Kar
,
A.
, and
Mazumder
,
J.
,
1996
, “
A Modeling Study on the Influence of Pulse Shaping on Keyhole Laser Welding
,”
J. Laser Appl.
,
8
, pp.
291
297
.
24.
Patel
,
R. S.
, and
Brewster
,
M. Q.
,
1991
, “
Gas-Assisted Laser-Metal Drilling: Theoretical Model
,”
J. Thermophys. Heat Transf.
,
5
, No.
1
, pp.
32
39
.
25.
Ready
,
J. F.
,
1965
, “
Effects Due to Absorption of Laser Radiation
,”
J. Appl. Phys.
,
36
, No.
2
, pp.
462
468
.
26.
Charschan, S. S., 1993, Guide to Laser Materials Processing, Laser Institute of America, p. 147.
You do not currently have access to this content.