Mathematical Modeling of Laser Beam Welding

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This project deals with the process of high energy beam welding. The first objective is to develop a realistic mathematical model which includes all of the important physics -- keyholing, nonequilibrium vaporization and subsequent vapor expansion, convection within the liquid region, and conduction within the solid region. The second objective is to develop a more efficient numerical scheme for computation. To achieve this objective, a modular approach will be employed. Different methods best suited for each specific region are to be used. Within the solid region the boundary element method will be used to solve for the heat transfer. Boundary layer theory will be applied to model the convection within the melt region. The nonequilibrium vaporization will be modeled with a Mott-Smith type solution. The subsequent vapor expansion will be modeled by a one- dimensional gas dynamic equation. These different regions are to be combined together by matching boundary conditions along the solid- liquid and liquid-vapor interfaces. The matching of boundary conditions along the solid-liquid interface determines its shape, hence the shape of the molten region. The matching of boundary conditions along the liquid-vapor interface determines the keyhole shape. It is expected that this technique will be computationally efficient and will provide more realistic predictions of the weld penetration, the molten shape, the cooling rate and the heat affected zone. Experiments will be performed to verify the mathematical model.