Scaling Laws for Melting and Resolidification in Direct Selective Laser Sintering of Metals 322

We present a one-dimensional model describing the physical mechanisms of heat transfer, melting and resolidification taking place during and after the interaction of a laser beam with a semi-infinite metal surface. The physical model describing this situation is based on the classical Stefan problem with appropriately chosen boundary conditions to reflect direct selective laser sintering of metals. A numerical model based on the finite volume method is developed to perform computations for different beam diameters, scan speeds, substrate temperatures and power input profiles. From the results of these computations, we derive relations for time to initiate melting, time to reach maximum melting depth, and total melt-resolidification time. The surface temperature histories for three different power input profiles are compared with approximate closed form solutions. INTRODUCTION Direct selective laser sintering (SLS) of metals is a process in which a high-energy laser beam directly consolidates a metal powder or powder mixture to full density. Melting and resolidification processes in direct SLS can have significant effect on the temperature distribution, residual stress, and the final microstructure quality of the parts. Therefore, it is essential to understand the response of melting and resolidification processes to time-dependent changes in heat flux input in order to implement real time laser power, beam diameter, and scan speed control. This is especially necessary to account for process perturbations that occur due to random variations in laser power, for different thermal boundary conditions e.g. whether a layer of powder has a previously solidified layer (conducting) or powder relatively insulating underneath it, as well as to account for variations in thermophysical, optical and material properties when multiple materials are used to make heterogeneous parts. There are several previous analytical and numerical studies for understanding this kind of phase change problem [1-10]. These studies considered only dynamics of the melting phenomena. However, both melting and resolidification as a function of time-dependent heat flux input are important for real time control of laser fusion based SFF processes. Furthermore, non-dimensional analyses of scaling laws between process variables and controlling parameters in such processes are especially useful in understanding process dynamics. In the future these laws can be incorporated into solidification models that can predict microstructure formation as a function of processing parameters. In this paper, a one-dimensional model that describes the physical mechanisms of heat transfer, melting and resolidification taking place during and after the interaction of a laser beam with a bed of pure metal powder approximated as a semi-infinite surface is presented. We conduct non-dimensional analysis of this process under various conditions. PHYSICAL MODEL In this paper, one-dimensional heat conduction with phase change in a solid of length L is considered. Heat flux from a laser flows in through the top surface during heat up while the