Depth of melt- pool and heat- affected zone in laser surface treatments
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dJd
~
p-1/2
_
(0 a
_
1) Q - '
where d is the laser beam width, 0~ is the ratio of "penetration temperature" to substrate farfield temperature, and P and Q are the dimensionless laser-scan speed and absorbed power, respectively. This scaling law, alternatively derived as an asymptotic limit of a classical closedform solution, applies for moderate scan speeds and power. Evidence that it captures the dominant experimental behavior in cases of no melting and melting is presented. The predicted depths also compare favorably to numerical simulations by finite elements (a three-dimensional (3D) workpiece of finite extent).
I.
INTRODUCTION
LASER surface treatment of metallic parts is recognized to have tremendous engineering potential since "tailoring" of surface properties can enhance performance as well as cut expense. A laser energy source typically modifies a thin region (scale of millimeters) beneath the surface of the metallic piece. Modifications range from "solid-state" changes such as annealing or transformation-hardening to melting/freezing changes as occur in surface alloying. Apart from the specifically tailored metallurgical properties, the most important characteristic of the modified layer is its depth of penetration which is related to the maximum temperature achieved during processing. Our interest is in the depth of the liquid pool in the case of melting, the depth of the transformation zone in the case of solid-state treatments, or both. More generally, we consider any of various depths determined by the penetration of a particular isotherm. The dependence of such depths on laser-scan speed and source strength, the principal control parameters, is the focus. See Reference 1 for a review of models of laser processing in general. There have been many studies of the depth of the heataffected zone and molten pools with varying emphases on experiments, modeling, and simulations. In the extreme, the experimental studies statistically analyze large numbers of measurements in order to develop a master correlation for purposes of predictionJ 21 For these, the laws of physics play little or no role in the analysis as the correlations are largely empirical. A disadvantage is that, without insight into which groups of variables should be plotted and against which other groups, the resulting correlations tend to be complicated and they often conceal the dominant physics. P.H. STEEN, Associate Professor, is with the School of Chemical Engineering and Center for Applied Mathematics, Cornell University, Ithaca, NY 14853. P. EHRHARD, Scientist, is with the Institut ffir Angewandte Thermo- und lZluiddynamik, and A. SCHI]SSLER, Scientist, is with the Institut for Material und Festk6rperforschung I, Kernforschungszentrum, Karlsruhe, Germany. Manuscript submitted August 3, 1992. METALLURGICAL AND MATERIALS TRANSACTIONS A
At the other extreme, the equations of mass, energy, and momentum conservation are solved computationally for temperatures (and velocities, etc., where appropriate) as a function of position and t
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