Thermal analysis of the laser surface transformation hardening process

Abstract An analytical solution for the temperature rise distribution in laser surface transformation hardening of a steel workpiece of finite width is developed based on Jaeger's classical moving heat source method [Proc. Roy. Soc. NSW 76 (1942) 203] and Carlsaw and Jaeger [Conduction of heat in solids, Oxford University Press, Oxford, UK, 1959] to predict the optimal operational parameters. The laser beam is considered as a moving plane (disc) heat source with a pseudo-Gaussian distribution of heat intensity. It is a general solution 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 temperature 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) and the hardening zone near the surface of the workpiece with finite width can 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. (December 1979) 456] reported a five level, full factorial experiments of laser surface transformation hardening. They considered the surface temperatures and the depth of hardening as approximate functions of the laser input parameters, namely, the laser beam power, P , the laser beam diameter, D e , and the traverse velocity of the beam, v . A comparative study is made on the analytical approach presented here with the multi-parameter experimental and 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, significant differences were found for the laser transformation hardening for a depth of hardening of 0.1 mm. This was due to the nature of the semi-empirical 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., power intensity) for no surface melting which has some physical significance, while it was assumed to be proportional to P 2 / D b for laser transformation hardening for a depth of hardening of 0.1 mm, for which there is no physical or analytical basis. Steen and Courtney developed semi-empirical equations based on the regression analysis of the experimental data, while the analytical solutions presented here are exact. The analytical solutions provide a better appreciation of the physical relationships between the relevant laser parameters and the width of the workpiece. The analysis facilitates the prediction and optimization of the process parameters for practical applications.