Tree-ring formation during vacuum arc remelting of INCONEL 718: Part II. Mathematical modeling

Tree-ring grain formations, a common microstructural feature found in vacuum arc remelted (VAR) ingots of nickel-based superalloys, were characterized experimentally in Part I. The experimental observations led to the conclusion that tree rings are chains of fine-equiaxed grains interrupting a predominately columnar-dendritic structure. Several possible mechanisms for their formation were considered, and their implications correlated with experimental observations. The most likely mechanism was determined to be that process perturbations cause changes in the thermal (or solutal) fields ahead of the columnar-dendrite tips, temporarily altering the conditions to increase grain nucleation and, hence, forming fine-equiaxed grains. In this article, Part II, a multiscale mathematical model of the VAR process is presented that simulates the macroscopic heat and momentum transport and combines it with a mesoscopic model of the nucleation and growth of grains. Using this multiscale model, the transient development of the VAR grain structure was simulated with varying levels and durations of fluctuations in the principal process parameters: power supply, arc focus, melt rate, and the ingot-crucible heat-transfer coefficient. The simulations were shown to agree with optical and electron back-scattered diffraction (EBSD) measurements of grain morphology and crystallographic orientation. The model results predict that tree-ring structures (consistent with those observed experimentally) can be formed by process perturbations that alter the thermal field conditions at the solidification front. A sensitivity study of the effect of the different process fluctuations on the microstructure formation was performed, providing process maps predicting the range of conditions where tree rings will not form.