Characterizing the Local Primary Dendrite Arm Spacing in Directionally Solidified Dendritic Microstructures

Abstract

Characterizing the spacing of primary dendrite arms in directionally solidified microstructures is an important step for developing process-structure-property relationships by enabling the quantification of (i) the influence of processing on microstructure and (ii) the influence of microstructure on properties. In this work, we utilized a new Voronoi-based approach for spatial point pattern analysis that was applied to an experimental dendritic microstructure. This technique utilizes a Voronoi tessellation of space surrounding the dendrite cores to determine nearest neighbors and the local primary dendrite arm spacing. In addition, we compared this technique to a recent distance-based technique and a modification to this using Voronoi tessellations. Moreover, a convex hull-based technique was used to include edge effects for such techniques, which can be important for thin specimens. These methods were used to quantify the distribution of local primary dendrite arm spacings, their spatial distribution, and their correlation with interdendritic eutectic particles for an experimental directionally solidified Ni-based superalloy micrograph. This can be an important step for correlating processing and properties in directionally solidified dendritic microstructures.

Evaluating Local Primary Dendrite Arm Spacing Characterization Techniques Using Synthetic Directionally Solidified Dendritic Microstructures

“…In an experimental microstructure, the primary dendrite cores are separated by a critical minimum distance that should scale with both the size of the dendrite stalk and the distance associated with the transition of tertiary to primary dendrite arms. For example, our previous study [33] shows that the dendrite stalk diameter is approximately 20 pct of the bulk PDAS (i.e., stalk diameter is twice the maximum distance at which no eutectic particles were observed). This prior result suggests that noise levels of 0:40a 0 are the highest noise level that might be observed in a real microstructure, because any higher noise level could produce neighboring points that lie within 0:20a 0 distance of each other.…”

“…[32] Previous work examined some recent approaches, as well as some modified versions of these approaches, for characterizing the local dendrite arm spacing within experimental dendritic microstructures. [33] This work used an experimental dendritic microstructure along with three different techniques that are based on the nearest neighbor spacing and/or a Voronoi tesselation of the dendrite cores. Figure 1 shows (a) an example of a directionally solidified dendritic microstructure [34] along with contour plots showing the evolution of the local PDAS as a function of dendrite location for four different techniques (to be discussed in Section II-B).…”

“…Figure 2 [34] The dots denote the dendrite cores, where the white dots indicate dendrite cores at the edge of the field of view. The local primary dendrite arm spacing (lm) was calculated using four different techniques: [33] (b) Voronoi tesselation with (blue) and edge points (red) for the large microstructures, whereby the edge points are selected using a small distance (1:5a 0 ) from edge of the microstructure pattern. The present analysis includes these edge points only for calculating the localized statistics of interior points, but does not use their localized statistics for subsequent mean statistics, heretofore also referred to as the bulk statistics.…”

“…In Figure 3, the different techniques for the same microstructure are shown from left to right (labels at the bottom), while the noise level is increased from top to bottom to illustrate the differences. The techniques presented in Figure 3 were first used together in Tschopp et al [33] to characterize the local spacing for an experimental microstructure of a directionally solidified single crystal nickelbased superalloy. In contrast to that work, the following work will examine the sensitivity and applicability of a few of these techniques based on thousands of synthetic microstructure instantiations.…”

“…Notice that the distance between the inner and outer circle tends to increase with increasing noise due to the increased d std of the nearest neighbors. As discussed in Tschopp et al, [33] clearly a method for restricting the number of nearest neighbors using such a technique is necessary.…”