Fluid Flow and Defect Formation in the Three-Dimensional Dendritic Structure of Nickel-Based Single Crystals

Abstract

Fluid flow within the dendritic structure at the solid-liquid interface in nickel-based superalloys has been studied in two directionally solidified alloy systems. Millimeter-scale, three-dimensional (3D) datasets of dendritic structure have been collected by serial sectioning, and the reconstructed mushy zones have been used as domains for fluid-flow modeling. Flow permeability and the influence of dendritic structure on flow patterns have been investigated. Permeability analyses indicate that the cross flow normal to the withdrawal direction limits the development of flow instabilities. Local Rayleigh numbers calculated using the permeabilities extracted from the 3D dataset are higher than predicted by conventional empirical calculations in the regions of the mushy zone that are prone to the onset of convective instabilities. The ability to measure dendrite surface area in 3D volumes permit improved prediction of permeability as well.

Cross-Permeability of the Semisolid Region in Directional Solidification: A Combined Phase-Field and Lattice-Boltzmann Simulation Approach

“…Figure 9 puts our results in contrast with the equations presented by Madison et al 18 and Poirier et al 17 For all three cases, the curves are shown for k 1 growth in the dendrite tip region and restricted growth below and (at least under these conditions) is wrongly predicted by the empirical relation of Poirier by up to a factor of 100 for high fraction liquid values. For prediction of fluid-flow phenomena in the upper part of the mushy zone (e.g., the initiation of freckles during electro-slag remelting (ESR)), 2 this can have significant consequences.…”

“…This can be easily explained by the fact that in our phase-field simulations, the primary dendrite distance k 1 was modified ''artificially'' without changing the local thermal parameters (temperature gradient and cooling rate). To the contrary, the formulae by Poirier 17 and Madison 18 assume the change of k 1 to be attributed to a change of the local thermal condition (i.e., they assume that the dendrites have selected their primary distance according to the local conditions). Thus, no similarity should be expected with respect to the k 1 -dependency of the cross-permeability because the main effect, which is the change of k 2 due to an altered local solidification time, has not been included in our study.…”

Development and application of a new freckle criterion for technical remelting processes

“…(8)). This seems to be in conflict with measurements of the freckle composition in alloy 718 implying that freckles are fed by a melt originating from a region in the mushy zone with a fraction liquid of about 0.4-0.6 [30,43]. However, it can be assumed that, even if freckles are initiated at considerably higher liquid fractions, they will erode the dendritic network, locally increase permeability, and thus penetrate downward deeper into the mushy zone.…”

“…8. In a first step, the dynamic permeability in isothermal direction was calculated using the Blake-Kozeny-relation as a function of the fraction liquid [43]:…”

Acquisition of Real-Time Operation Analytics for an Automated Serial Sectioning System

“…Spowart and Mullens later developed an automated approach to serial sectioning by combining a 6-axis robot arm, an inverted optical microscope, an ultrasonic bath, and a polishing wheel with interchangeable diamond abrasive films. This system was shown to successfully serial-section a variety of material systems [16][17][18][19][20][21][22]. UES, Inc. later purchased the rights to license this tool, commercialized the product, and have deployed units worldwide [23].…”