Modelling deep penetration laser welding using a BEM sensitivity scheme

The process of deep penetration welding is modelled by dividing the problem into three sub-regions: solid, liquid and vapor. Each of these sub-regions are analyzed individually by the most suitable method. By matching these three solutions with appropriate boundary conditions, a complete model is obtained. The boundary element method (BEM) is used to simulate the heat transfer within the solid region. Lubrication theory is applied to model the heat transfer within the liquid. The non-equilibrium vaporization and subsequent gas dynamics are modelled by a one-dimensional model. This paper presents a BEM formulation for three-dimensional steady-state convection-conduction problems and a BEM sensitivity formulation for the determination of sensitivities of temperature and heat flux due to a boundary shape parameter. The BEM sensitivity formulation is based on the direct differentiation approach (DDA). These formulations are applied to simulate deep penetration welding. It is found that the BEM and the sensitivity formulation are very efficient and robust in the determination of the solid-liquid interface in a workpiece.