A semi-analytical method based on the Green's function for the laser melting process of the metal materials

Thermal responses of the metal materials subjected to intense laser irradiation are complicated due to the phase change in the melting process. In order to simplify this problem, previous studies usually ignored the liquid phase or took the usage of finite element method, which limited the achievement of theoretical breakthroughs. In the present study, a one-dimensional heat transfer model with consideration of phase change was established to describe the melting process of the metal materials caused by a constant intense laser beam. The governing equations with three domains were constructed in the piecewise form: the liquid phase region (melted already), the solid phase region (unmelted yet) and the melting region. The limited discretization method was employed to describe the moving of the soli-liquid interface and the energy exchange. The piecewise governing equations in liquid and solid region were solved separately and analytically by means of the Green's function method, and the calculation result was verified by the finite element simulation. The results of the analytical model were in good agreement with those of the finite element simulation, and the maximal prediction errors of the temperature field prediction between the theoretical model and FE simulation is limited to 2.8 %. In addition, the influences of heat source intensity, material heat conductivity, latent heat on the melting process were discussed in detail. The analytical and simulation results reveal that the semi-analytical solution in piecewise for 1-D laser melting process can be successfully used to reflect the dynamic temperature response of the metal materials and the movement of the solid-liquid interface. This work is of guiding significance for the analytical solution of the multi-dimensional melting process of the metal materials under the fixed and continuous laser beams.