A mathematical model for penetration laser welding as a free-boundary problem

A detailed model is constructed in order to determine the full 3D weld pool and keyhole geometry by setting the appropriate energy and pressure balances. The energy balance takes into account heat conduction, ablation losses and evaporation effects at the keyhole open surfaces, as well as the most relevant energy-absorption mechanisms, namely Fresnel and inverse Bremsstrahlung. The pressure balance ensures mechanical stability of the keyhole by including ablation pressure against surface tension pressure. The model provides a full description of the temperature field, electronic density, degree of ionization and absorption coefficient within the plasma, as well as setting the maximum penetration depth for a given set of laser parameters such as power, focusing radius and oscillation transversal mode. The keyhole boundary is initially taken to be an unknown free boundary and is obtained as a part of the solution of the problem. For low and medium welding speeds this boundary is successfully described with a family of ovoids. Good agreement with experimental results is achieved for a wide range of laser powers and plate thicknesses.