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57. D. Lacroix, G. Jeandel, C. Boudot, Solution of the radiative transfer equation in an absorbing
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44. K.C. Mills, Recommended values of thermophysical properties for selected commercial
alloys, in ASME International (2002), p. 189
45. C.J. Smithells, E.A. Brandes, Metals Reference Book, 7th edn. (Reed Educational and
Professional Publishing Ltd., 1992)
46. J.M. Jouvard, K. Girard, O. Perret, Keyhole formation and power deposition in Nd: YAG laser
spot welding. J. Phys. D: Appl. Phys. 34, 2894–2901
47. Z. Wenhai, Modeling the formation and collapse of a keyhole during laser welding process.
Ph.D. thesis (University of Missouri-Rolla, 2002), pp. 125–127
48. M. Mizutani, S. Katayama, Keyhole behavior and pressure distribution during laser irradiation
on molten metal, in ICALEO, Section A (2003), pp. 149–167
49. S. Katayama, N. Seto, J. Kim et al., Formation mechanism and suppression procedure of
porosity in high power laser welding of aluminum alloys, in ICALEO, Section C (1998),
pp. 24–33
50. N. Seto, S. Katayama, A. Matsunawa, A high-speed simultaneous observation of plasma
and keyhole behavior during high power CO 2 laser welding, in ICALEO, Section E (1999),
pp. 19–27
51. A. Matsunawa, S. Katayama, J. Kim et al., Dynamics of keyhole and molten pool in high
power laser welding. J. Laser Appl. 10(6), 247–254 (1998)
52. N. Seto, A. Matsunawa, S. Katayama et al., High-speed simultaneous observation of plasma
and keyhole behavior during high power CO 2 laser welding: effect of shielding gas on porosity
formation. J. Laser Appl. 12(6), 245–250 (1998)
53. N. Seto, S. Katayama, M. Mizutani et al., Formation mechanism of porosity in high power
YAG laser welding, in ICALEO, Section A (2000), pp. 16–25
54. C. Tix, G. Simon, A transport theoretical model of the keyhole plasma in penetration laser
welding. J. Phys. D: Appl. Phys. 26, 2066–2074 (1993)
55. J. Wang, X. Wang, J. Shen, Calculative pattern of laser welding stability for titanium alloys.
Trans. China Weld. Inst. 21(4), 13–16 (2000)
56. J. Greses, P.A. Hilton, G.Y. Barlow et al., Plume attenuation under high power Nd: yttriumaluminum-gamet laser welding. J. Laser Appl. 16(1), 9–15 (2004)
57. D. Lacroix, G. Jeandel, C. Boudot, Solution of the radiative transfer equation in an absorbing
and scattering Nd: YAG laser-induced plume. J. Appl. Phys. 84, 2443 (1998)
58. J. Zhou, H.L. Tsai, T.F. Lehnhoff, Investigation of transport phenomena and defect formation
in pulsed laser keyhole welding of zinc-coated steels. J. Phys. D: Appl. Phys. 39(24), 5338–
5355 (2006)
59. S. Pang, A Study on the Transient Keyhole and Moving Weld Pool Behaviors and Mechanisms of
Deep Penetration Laser Welding (Huazhong University of Science and Technology (HUST),
Wuhan, 2011)
60. H. Ki, P.S. Mohanty, J. Mazumder, Modeling of laser keyhole welding: Part I. Mathematical modeling, numerical methodology, role of recoil pressure, multiple reflections, and free
surface evolution. Metall. Mater. Trans. A 33, 1817–1830 (2001)
61. H. Ki, P.S. Mohanty, J. Mazumder, Modeling of laser keyhole welding: Part II. Simulation of
keyhole evolution, velocity, temperature profile, and experimental verification. Metall. Mater.
Trans. A 33, 1831–1842 (2001)
62. J.H. Cho, S.J. Na, Three-dimensional analysis of molten pool in GM A-laser hybrid welding.
Weld. J. 88(2), 35–43 (2009)
63. J.-H. Cho, S.-J. Na, Implementation of real-time multiple reflection and fresnel absorption of
laser beam in keyhole. J. Phys. D: Appl. Phys. 39(24), 5372–5378 (2006)
64. S. Osher, R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer, Berlin,
2002)
65. A. Matsunawa, V.Y. Semak, The simulation of front keyhole wall dynamics during laser
welding. J. Phys. D: Appl. Phys. 30(5), 798–809 (1997)
66. V. Semak, A. Matsunawa, The role of recoil pressure in energy balance during laser materials
processing. J. Phys. D: Appl. Phys. 30(18), 2541–2552 (1997)