A Closed-Form Solution for the Effect of Free Edges on Melt Pool Geometry and Solidification Microstructure in Additive Manufacturing of Thin-Wall Geometries

Laser and electron beam-based additive manufacturing of Ti-6Al-4V are under consideration for application to aerospace components. A critical concern for these processes is the ability to obtain a consistent and desirable microstructure and corresponding mechanical properties of the deposit. Based on the Rosenthal solution for a moving point-heat source, recent work has developed simulation-based process maps for the thermal conditions controlling microstructure (grain size and morphology) in beam-based deposition of semi-infinite geometries, where a steady-state melt pool exists away from free edges. In the current study, the Rosenthal solution is modified to include the effects of free edges. This is accomplished by the superposition of two point-heat sources approaching one another, with the line of symmetry representing the free edge. The result is an exact solution for the case of temperature-independent properties. Dimensionless results for melt pool geometry are determined, and plotted as a function of distance from the free edge. Results are plotted on solidification maps to predict trends in microstructure for Ti-6Al-4V. Finite element analysis is used to verify results. Results suggest that melt pool geometry is more sensitive to free edges than solidification microstructure.