Erratum to: A Coupled Thermal, Fluid Flow, and Solidification Model for the Processing of Single-Crystal Alloy CMSX-4 Through Scanning Laser Epitaxy for Turbine Engine Hot-Section Component Repair (Part I)

Scanning laser epitaxy (SLE) is a new laser-based additive manufacturing technology under development at the Georgia Institute of Technology. SLE is aimed at the creation of equiaxed, directionally solidified, and single-crystal deposits of nickel-based superalloys through the melting of alloy powders onto superalloy substrates using a fast scanning Nd:YAG laser beam. The fast galvanometer control movement of the laser (0.2 to 2 m/s) and high-resolution raster scanning (20 to 200 µm line spacing) enables superior thermal control over the solidification process and allows the production of porosity-free, crack-free deposits of more than 1000 µm thickness. Here, we present a combined thermal and fluid flow model of the SLE process applied to alloy CMSX-4 with temperature-dependent thermo-physical properties. With the scanning beam described as a moving line source, the instantaneous melt pool assumes a convex hull shape with distinct leading edge and trailing edge characteristics. Temperature gradients at the leading and trailing edges are of order 2 × 105 and 104 K/m, respectively. Detailed flow analysis provides insights on the flow characteristics of the powder incorporating into the melt pool, showing velocities of order 1 × 10–4 m/s. The Marangoni effect drives this velocity from 10 to 15 times higher depending on the operating parameters. Prediction of the solidification microstructure is based on conditions at the trailing edge of the melt pool. Time tracking of solidification history is incorporated into the model to couple the microstructure prediction model to the thermal-fluid flow model, and to predict the probability of the columnar-to-equiaxed transition. Qualitative agreement is obtained between simulation and experimental result.