Modeling Melt Pool Geometry in Metal Additive Manufacturing Using Goldak's Semi-Ellipsoidal Heat Source: A Data-driven Computational Approach

This analytical solution, based on Goldak's Semi-Ellipsoidal Heat Source model, captures the dynamic temperature evolution from a semi-ellipsoidal power density moving heat source within a semi-infinite body. It tackles the convection-diffusion heat transfer equation by integrating an instantaneous point heat source across the volume of the ellipsoidal shape. The model's precision is validated by the excellent match between the predicted transient temperatures and empirical data from bead-on-plate specimens, enhancing its capability to accurately predict in-process temperature profiles in laser-based metal additive manufacturing (AM) operations. Developed in Python, the model offers customized calculations from setup to boundary conditions, adapting to variations in material properties under intense heat gradients. It considers the temperature dependency of thermal material properties and AM-process parameters, accounting for significant temperature gradients and changes in heat transfer mechanisms. The model also includes phase changes of melting or solidification with adjusted heat capacity to accurately reflect these transformations. Additionally, it considers the effects of variable laser power, scanning speed, and timing across each scanning pattern segment, acknowledging the thermal interactions between successive layers and their impact on heat transfer. This comprehensive analytical model is ready for applications including thermal stress analysis, microstructure modeling, and simulation of AM processes, predicting residual stresses and distortions.