Surface depression and ablation for a weld pool in material processing: A mathematical model

Abstract

In the process of CW laser welding the action of the laser generates a weld pool in the work piece which undergoes translation. Additionally, complicated flows of molten material occur. The weld pool would be hemispherical in shape if it were at rest relative to the laser beam. In the interests of simplicity this case of a hemispherical weld pool will be studied here, neglecting the flow in the weld pool and the effect of translation on the work piece. A small top part of the free surface of the weld pool in the form of a circular spot is subjected to the action of the laser beam. This spot will be assumed to be maintained at the vaporisation temperature of the material, while outside the spot the usual no-heat-flux boundary condition will apply with the shape of the top surface of the weld pool limited by the assumed circular melting isotherm. These conditions on the top of the weld pool surface therefore generate a problem with mixed boundary conditions. The heat conduction equation will then be solved in the weld pool to determine the temperature of its free surface. The liquid free surface of the weld pool is subject to a process of quasi-equilibrium ablation as an evaporation front moves into air under ambient conditions above the surface in the laser case. A Knudsen layer exists above the molten region extending for a few mean free paths and a discontinuous change of temperature, pressure and density occurs across the evaporation front with the flow of hot vapour propagating as a shock wave into the air above. This ablation process is modelled and the surface depression calculated. With some modifications similar considerations apply to the case of electric arcs.In the process of CW laser welding the action of the laser generates a weld pool in the work piece which undergoes translation. Additionally, complicated flows of molten material occur. The weld pool would be hemispherical in shape if it were at rest relative to the laser beam. In the interests of simplicity this case of a hemispherical weld pool will be studied here, neglecting the flow in the weld pool and the effect of translation on the work piece. A small top part of the free surface of the weld pool in the form of a circular spot is subjected to the action of the laser beam. This spot will be assumed to be maintained at the vaporisation temperature of the material, while outside the spot the usual no-heat-flux boundary condition will apply with the shape of the top surface of the weld pool limited by the assumed circular melting isotherm. These conditions on the top of the weld pool surface therefore generate a problem with mixed boundary conditions. The heat conduction equation will then be solved ...