Response of primary dendrite spacing to varying temperature gradient during directional solidification

Abstract

The response of primary dendrite spacing to a change in solidification condition is examined through the directional solidification of a succinonitrile-acetone alloy. While the growth velocity was kept constant, the thermal gradient G was alternately varied between two extreme values. The measured average dendrite spacing is compared to a calculation involving a previously proposed model, revealing good correlation. The investigation results enable us to characterize some important features about dendrite spacing evolution: during alternately changing G, dendrite spacing varies along different paths; after changing G-variation direction at turning points, the incubation periods required for the initiation of variation are much longer than those at the initial stage; as G changes back to its initial state, cannot return to its original value, revealing an unclosed hysteresis loop for the -G diagram; and continuing the process of alternately changing G will result in the formation of a closed loop. This kind of hysteresis loop is repeatable and roughly the same for varying G in reverse sequences. Thus, becoming free of the effect of the initial state, varies in nearly the same way for the same change in process condition, regardless of the difference in previous history.

On Directional Dendritic Growth and Primary Spacing—A Review

“…It could quantitatively calculate the minimum, maximum and average λ 1 in response to a change in V from an initial stage of stable growth. Following this, Ma [127] extended the model to predict the λ 1 distribution with varying G, whilst the V remained constant. The results between both analytical models demonstrated the same intrinsic λ 1 relationship and a good fit with experimental data [114].…”

“…Currently, the lower stability bound for a fixed set of growth conditions has received a proper theoretical treatment and is predicted analytically [103] and numerically [107] with good accuracy (Figure 8). The upper stability bound is understood from an analytical point of view [41,126,127]. Unfortunately, the mechanisms behind local dendritic misorientation and its influence on the upper λ 1 selection procedure are not fully understood.…”

Three-Dimensional Multiscale Modeling of Dendritic Spacing Selection During Al-Si Directional Solidification

“…11 Other models of spacing selection have been proposed based on geometrical arguments. 12,13 Those latter models assume steady-state growth dynamics and estimate the upper limit of stable spacing K max to be about twice the lower limit K min , 12 while recent numerical studies have predicted a ratio K max =K min closer to three or four. 14,15 (For a brief review of primary spacing selection theory, see Sect.…”

Patterns in Directionally Solidified Alloys

“…Currently, the lower stability bound for a fixed set of growth conditions has received a proper theoretical treatment and is predicted analytically 122 and numerically 126 with good accuracy (Figure 2-8). The upper stability bound is understood from an analytical point of view 51,144,145 .…”