2D and 3D phase-field simulations of lamella and fibrous eutectic growth

Abstract

The coupled eutectic growth of binary alloys was studied by means of phase-field models or boundary integral methods for many years. The use of numerical methods discovered the remarkable variety of growth structures like lamellae or different kinds of oscillating modes. In this work, the multi-phase-field method which is generally valid for most kinds of transitions between multiple phases is applied to the eutectic growth problem. We simulated the directional solidification of a binary eutectic during the initial transient state in 2 and 3 dimensions. The chosen phase diagram of the eutectic alloy is asymmetric with a composition ratio between the two solid phases α and β of 0.82. The 2D simulations show stable lamella growth or unstable oscillating modes dependent on the number of β lamella specified by explicit seeding at the bottom of the calculation domain. The undercooling at the growth front is evaluated for different spacing and compared with the values obtained by the fundamental analysis for the steady-state growth via the Jackson and Hunt model. For the regular lamella growth, the undercooling evaluated from the phase-field simulations fits within 20% of the analytical values. 3D calculations show the fibrous growth structure. This is in agreement with the expectation because for small phase fractions of β the fibrous structure possesses a smaller total amount of surface energy compared with lamellas and therefore should be preferred. For a larger number of fibres, they tend to form a hexagonal arrangement which is usually observed by experiments.