Keyhole formation
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I.
INTRODUCTION
T H E size and temperature distribution across the melt pool and the keyhole are important to the theorist who is attempting to describe by various combinations of conduction and convection, the thermal profiles that result from high energy density welding. Such thermal profiles can and have been utilized to calculate the volume fraction of phases that occur in the weldment and heat-affected zones. This article describes a methodology to calculate the size and temperature across the keyhole. But the article, first, points out an internal inconsistency in the literature concerning surface tension and keyhole size.
II.
SURFACE TENSION
Analysis of the forces m acting in the keyhole indicate that the vapor pressure acts to keep the keyhole open, whereas the pressure from the surface tension and gravitational forces acts to close the keyhole. This can be expressed as ffA = T + pgh
[1]
r
where PA = the partial vapor pressure of element A in the gas phase; 7 = the surface tension of element A; r = the radius of the keyhole; p = the density of the liquid phase of element A; and g = the gravitational constant. Denney and Metzbower t2j have shown that the diameter of the keyhole is very close to the diameter of the focused laser beam. This is based on videotapes of the molten pool of laser beam weldments of stainless steel and steels in which the plasma obscures only an area that is approximately the same as that of the focused beam E.A. METZBOWER, Supervisory Metallurgist, is with the United States Naval Research Laboratory, Washington, DC 20375-5343. Manuscript submitted March 10, 1992. METALLURGICAL TRANSACTIONS B
area. These same videotapes also indicate that the position of this interaction is below the surface of the plate. The diameter of the focused laser beam was estimated by revolving a nonconductive material under the laser beam at a high speed. In high power laser beam welding, the diameter of the laser beam depends on the power, the quality of the optics, and the beam mode and can vary from 0.1 to 2 m m in diameter. Most high power lasers yield a focused laser beam diameter of about 1 mm. The value of the surface tension for pure metals is listed in references, such as Smithells. t3~ The surface tension for pure metals is a decreasing function of temperature. Using this data and assuming that the keyhole is on the top surface of the plate (no hydrostatic force), the vapor pressure required to keep the keyhole open to the diameter of the beam can be calculated. Knowing the required vapor pressure, the temperature necessary to create this vapor pressure can also be calculated. This data is tabulated in Table I. Table I gives the metal, the temperature at which the surface tension has been calculated, the pressure (in millimeters Hg) that corresponds to that surface tension, a I-ram-diameter keyhole, and finally the temperature which is required for that pressure to exist. The last column has been calculated from the data of Hultgren et al.,[4] which lists the vapor pressure as a function o
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