A MATHEMATICAL-MODEL FOR PENETRATION LASER-WELDING AS A FREE-BOUNDARYPROBLEM

A detailed model is constructed in order to determine the full 3D weld pool and keyhole geometry by setting the appropriate energy and press ure balances. She energy balance takes into account heat conduction, a blation losses and evaporation effects at the keyhole open surfaces, a s well as the most relevant energy-absorption mechanisms, namely Fresn el and inverse Bremsstrahlung. The pressure balance ensures mechanical stability of the keyhole by including ablation pressure against surfa ce tension pressure. The model provides a full description of the temp erature field, electronic density, degree of ionization and absorption coefficient within the plasma, as well as setting the maximum penetra tion depth for a given set of laser parameters such as power, focusing radius and oscillation transversal mode. The keyhole boundary is init ially taken to be an unknown free boundary and is obtained as a part o f the solution of the problem. For low and medium welding speeds this boundary is successfully described with a family of ovoids. Good agree ment with experimental results is achieved for a wide range of laser p owers and plate thicknesses.