Three-Dimensional Multiphase Field Modeling of the Effect of Lamellar Thickness on the Eutectic Growth
- PDF / 562,729 Bytes
- 5 Pages / 593.972 x 792 pts Page_size
- 31 Downloads / 213 Views
NTRODUCTION
EUTECTIC growth is one of the most interesting topics in materials science and always attracts much attention.[1–3] A typical morphology in eutectics named lamellar eutectic has been studied widely based on the classic Jackson–Hunt (J-H) model to investigate the relationships between interface undercooling, growth rate, and lamellar spacing.[4] In the past, most of the experimental and theoretical studies on the lamellar growth were aimed at quasi-two-dimensional (2-D) thin samples. However, recently, some experimental and numerical studies on three-dimensional (3-D) bulk samples show that the microstructure in three dimensions is far different from that in two dimensions and the stability thresholds of lamellar patterns in bulk samples reduce obviously.[5,6] The phase-field method has become a powerful tool to simulate the microstructure formation during solidification. Recent progress on model formulation and numerical implementation makes it now possible to simulate the evolution of complex 3-D microstructure. Some work on eutectic growth in three dimensions has come forth by phase-field method.[6–11] A 3-D study conducted by Apel et al.[6] showed that phase field modeling can produce rodlike structures. Lewis et al.[7,8] reported that rod structures are preferred over lamellar structures when the minor phase volume fraction is less than approximately 0.3. Danilov and Nestler[9,10] presented an adaptive finite element method to simulate the growth of complex eutectic solidification in binary and ternary alloys. Regular oscillatory growth structures are observed together with a topological change of the matrix phase in three dimensions. Plapp and Parisi[11,12]
simulated the stability of 3-D lamellar eutectic growth through a multiphase field model, and they found that, over the entire composition range, the first instability to occur is a zigzag instability. Furthermore, Meng[13] et al.’s experimental results have also proved that the sample thickness has great effects on the eutectic morphology during directional solidification of CBr4C2Cl6 bulk sample. However, by now, the systematic study, especially the work on the effect of sample thickness on lamellar eutectic through numerical simulation, is still absent. The model proposed by Kim et al.,[14] which has an advantage in that the chemical potential is continuous and equal inside the interface over other multiphase models mentioned previously, has been confirmed effective and fruitful in 2-D simulation. Therefore, in this article, the effect of lamellar thickness on the morphology stability during the process of lamellar eutectic growth will be studied in three dimensions using the KKSO multiphase field model on the basis of benchmark results in two dimensions.
II.
MULTIPHASE FIELD MODEL
The detailed derivation of the KKSO multiphase field model used in this article can be found in Reference 14. The main ideas of this model are as follows. (1) Defining the function of the bulk free energy of the system: !# Z " X fP þ fT þ kL /i 1 dV ½1 F¼ V
where f P ¼
Ph i6
Data Loading...
