Prediction of Secondary‐Dendrite Arm Spacing for Binary Alloys by Means of a Phase‐Field Model

Abstract

The mechanical properties and performance of metal materials depend on the intrinsic microstructures in these materials. In order to develop engineering materials as expected and to enable design with multifunctional materials, it is essential to predict the microstructural patterns, such as size, shape, and spacing of the dendritic structures observed in solidified metals. In materials science and related areas, the phase‐field model is widely used as one of the powerful computational methods to simulate the formation of complex microstructures during solidification and phase transformation of metals and alloys. In the present study, the secondary‐arm spacing for Fe–C binary alloys is numerically predicted using a phase‐field model in a two‐dimensional domain. When compared both with data by Ode et al. and with experimental data, the arm spacing predicted in the present work showed excellent agreement. Our estimates are performed at the late stage of growth. The change in arm spacing is examined both by changes of cooling rates and of local solidification time. A relation between material properties and model parameters is presented. Two‐dimensional simulations produced dendrites that are similar to the ones found in experiments reported in the literature. Through numerical examples, applicability of the phase‐field model to the problems of secondary‐dendrite arm spacing in Fe–C alloys is demonstrated.