Two-dimensional multi-scale dendrite needle network modeling and x-ray radiography of equiaxed alloy solidification in grain-refined Al-3.5 wt-%Ni

Abstract

The aim of this work is to investigate multiple dendritic equiaxed grain formation during directional solidification of grain-refined Al-3.5 wt-%Ni under a range of different solidification conditions. This is achieved by comparing the results of in-situ x-ray radiographic experiments involving thin samples (as reported in the literature) to the results of 2D multi-scale dendrite needle network (DNN) modeling covering the essential experimental length scale. The model takes into account heterogeneous nucleation, branched dendritic growth and solutal interaction between branches and multiple equiaxed grains. The decrease in equivalent circular diameter of the steady-state average grain size with pulling velocity, as observed in the Bridgman-type experiments, is well captured by the modeling results, and likewise the ratio of activated nucleation seeds. Using experimentally estimated nucleation parameters in the modeling, a log normal nucleation undercooling distribution provided slightly but not significantly better agreement with experiments than a Gaussian distribution, with remaining absolute differences in the equivalent circular diameter of up to 31%. Thus, even with the 2D modeling of an essentially 3D experiment, fairly good agreement is achieved. This is attributed to a solutal undercooling of the equiaxed front region in the modeling which is similar in comparison to the dendrite tip undercooling predicted by an analytical 3D calculation, on which the estimation of nucleation parameters was based. Moreover, dendrite side-branching in modeling is of minor impact, due to a ratio between solutal diffusion length and equivalent circular diameter inferior to 0.49 under all solidification conditions. Additionally, at low pulling velocities, the computed grain density is only slightly dependent on which unknown dendrite selection parameter σ* over a wider range is selected. On the other hand, at high pulling velocities there is no dependence. In short, application of the DNN model has proven to be adequate to the goal aimed at, with enhanced computational efficiency at the experimental length scale and given insight in the relevance of various physical phenomena and modeling parameters. The extension of the DNN model to the third dimension and larger Péclet number, reported very recently in literature, is expected to provide even better agreement.