Primary-dendrite-pattern regulation by secondary branch during the directional solidification of the single crystal superalloy

The dendrite array by directional solidification determines the mechanical properties of the single crystal superalloy. Achieving precise and effective control over the directional dendrite array has been challenging due to a lack of understanding the underlying mechanism. The study found that secondary branches with specific orientations play a significant role in determining the arrangement pattern of primary dendrites on the transverse section. These secondary branches induce either a unidirectional or bidirectional aligned pattern in the primary dendrite array. The proportion of aligned dendrites increases with the solidification distance, but decreases with the withdrawal velocity. The competitive growth coefficient of secondary branch was proposed based on the effectiveness components of thermal gradient. This coefficient is determined by the convexity of the liquid-solid interface, the angle between the primary arm and the vertical direction, and the orientations angle of secondary branch. The presence of a large competitive coefficient at the liquid-solid interface edge near the crucible gives secondary branches an advantage in growth. This leads to the development of tertiary arms which further grow into the main trunks, aligning parallel to the primary dendrites and forming the aligned pattern. Additionally, based on the competitive coefficient, the formation criterion and distribution law of dendritic pattern transitions were summarized. This provides effective guidance not only for controlling dendrite arrangement but also for estimating the single crystal orientation through visual inspection by back-calculating the formation criterion.