Prediction of grain structure evolution during rapid solidification of high energy density beam induced re-melting

Highlights: • A phase-field (PF) formulation considering both boundary curvature and thermal gradient driving forces is presented • The model is coupled with a thermal-fluid solution for the prediction of temperature fields and their spatial gradients • The model is validated against analytically predicted boundary positions for a single boundary in a linear field • The proposed solution approach is applied to various laser welding scenarios • Incorporating thermal gradient driving forces into the PF model is crucial for the prediction of micro-structural evolution Grain boundary migration in the presence of concentrated sources of heat is a complex process that has a considerable impact on resultant material properties. A phase field model is presented incorporating thermal gradient and curvature driving force terms to predict how a poly-crystalline network evolves due to the application of such heat sources, as grain boundaries migrate due to local boundary curvature and time-varying thermal gradients. Various thermal scenarios are investigated, in both two and three dimensions. These scenarios include both partial and full penetration laser induced melting, the application of a linearly varying time-independent thermal field, and successive melting events where regions experience multiple melting and solidification cycles. Comparisons are made between the microstructures predicted by the proposed phase field method, during the various thermal scenarios, that agree with commonly observed phenomena. Particularly interesting is the ability to explain the differences in grain morphology between the full penetration and partial penetration welds using the phase field model and associated driving force magnitudes between the two scenarios. The model predicts the restoration of grain boundary networks in regions experiencing multiple melting events, and explains the differences in grain morphology due to the local curvature and thermal gradient effects.