Trial for Estimation of One-dimensional Fraction Solid in the Horizontal Cross Section of Unidirectionally Solidified Specimen

Abstract

In order to clarify the location of secondary inclusions formed during solidification, this study proposed a function to estimate the one-dimensional fraction solid at any position from the cross-section of unidirectionally solidified specimen. The function is based on an n-th order function expressed as a combination of the dimensionless distance (r/R) defined within the dendritic domain and the rotation angle θ measured from a specific secondary branch. The function has a simple form and uses only one parameter but the estimated values of fraction solid are ideal both for one-dimensional and two-dimensional ones. In addition, the predicted shape of the cross-sectional structure of the dendrite that can be derived from the proposed function is reasonable. It was also revealed that it is possible to express a variety of shapes from a cell shape without secondary branches to a dendrite shape with well-developed secondary branches, by changing the value of parameter n.