Thermal analysis of the laser surface transformation hardening process

An analytical solution for the temperature rise distribution in laser surfa ce transformation hardening of a steel workpiece of finite width is develop ed based on Jaeger's classical moving heat source method [Proc. Roy. Sec. N SW 76 (1942) 203] and Carlsaw and Jaeger [Conduction of heat in solids, Oxf ord University Press, Oxford, UK, 1959] to predict the optimal operational parameters. The laser beam is considered as a moving plane (disc) heat sour ce with a pseudo-Gaussian distribution of heat intensity. It is a general s olution in that it is applicable for both transient and quasi-steady state conditions. The effect from two boundaries of the workpiece of finite width is included in the analysis. The solution can be used to determine the tem perature rise distribution in and around the laser beam heat source on the work surface as well as with respect to depth at all points including those very close to the heat source. The width and depth of the melt pool (MP) a nd the hardening zone near the surface of the workpiece with finite width c an also be calculated under transient and quasi-stationary conditions. The analytical model developed here can be used to determine the time required for reaching the quasi-steady state. Steen and Courtney [Metals Technol. (D ecember 1979) 456] reported a five level, full factorial experiments of las er surface transformation hardening. They considered the surface temperatur es and the depth of hardening as approximate functions of the laser input p arameters, namely, the laser beam power, P, the laser beam diameter, D-e, a nd the traverse velocity of the beam, v. A comparative study is made on the analytical approach presented here with the multi-parameter experimental a nd the semi-empirical approach by Steen and Courtney. While good agreement was found between the results of the analytical work and the semi-empirical approach for the case of scanning velocity for no surface melting, signifi cant differences were found for the laser transformation hardening for a de pth of hardening of 0.1 mm. This was due to the nature of the semi-empirica l relationships considered by Steen and Courtney for each case. For example , the traverse velocity was assumed to be proportional to P/D-b(2) (i.e., p ower intensity) for no surface melting which has some physical significance , while it was assumed to be proportional to P-2/D-b for laser transformati on hardening for a depth of hardening of 0.1 mm, for which there is no phys ical or analytical basis. Steen and Courtney developed semi-empirical equat ions based on the regression analysis of the experimental data, while the a nalytical solutions presented here are exact. The analytical solutions prov ide a better appreciation of the physical relationships between the relevan t laser parameters and the width of the workpiece. The analysis facilitates the prediction and optimization of the process parameters for practical ap plications. (C) 2001 Elsevier Science Ltd. All rights reserved.