Finite element simulation of laser surface treatments including convection in the melt pool

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Abstract
A two‐dimensional, macroscopic, stationary, finite element model is presented for both laser remelting and laser cladding of material surfaces. It considers, in addition to the heat transfer, the important fluid motion in the melt pool and the deformation of the liquid—gas interface. The velocity field in the melt is driven by thermocapillary forces for laser remelting, but also by forces due to powder injection for laser cladding. For a given velocity field within the liquid region, the stationary enthalpy (or Stefan) equation is solved. An efficient scheme allows the LU decomposition of the finite element matrix to be performed only once at the first iteration. Then, the velocity is updated using the Q1—P0 element with penalty methods for treating both the incompressibility condition and the slip boundary conditions. Numerical results for three different processing speeds for both laser remelting and laser cladding demonstrate the efficiency and robustness of the numerical approach. The influence of the thermocapillary and powder injection forces on the fluid motion and subsequently on the melt pool shape is seen to be important. This kind of calculations is thus necessary in order to predict with precision the temperature gradients across the solidification interface, which are essential data for microstructure calculations.

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