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.

Numerical Simulation of Microstructural Evolution via Phase-Field Model Coupled to the Solutal Interaction Mechanism

“…The concentrations in the solid indicate the presence of a microsegregation pattern. It should be observed that the phase-field calculations physically reproduces competitive growth of the columnar grains from the perturbed interface (Figure 9(a) and Figure 9(b)), the final arms spacing are independent of initial conditions, as discussed in [22]. On the other hand, spacing between columnar grains depends on the competitive growth of them during solidification.…”

“…The copper concentration in solid is much less than that of copper in liquid. All the columnar dendritic grains are growing from left surface but the shapes of the arms are different from each other due to the imposed noise by Equation (22). In this simulation, a fine solid layer was added to left side of the domain boundaries.…”

“…. For the binary alloy system, we use the same parameters shown in the [22]. To simulate growth of an asymmetrical dendrite, it is necessary to introduce a noise term on the right-hand side of Equation (13), the phase-field equation.…”

“…Several different numerical approaches were proposed to that end. Some works have focused on pure materials [16]- [18], whereas others take heed of multicomponent alloys of metallurgical interest [1] [19]- [22]. In particular, the phase-field model has garnered wide acceptance, given its ability to simulate the solidification process in the presence of a complicated solid-liquid interface.…”

Predicting Secondary-Dendrite Arm Spacing of the Al-4.5wt%Cu Alloy During Unidirectional Solidification

“…(1), the phase-field equation. A usual expression for this noise, as indicated by Ferreira et al 13 , is…”