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

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.