Phase-field model with relaxation of the partition coefficient

Abstract

Most phase-field models (PFMs) for diffusional phase transformation in alloys employ the equal diffusion potential (EDP) condition to eliminate the contribution of bulk free energies to the interface energy. For engineering alloys where their thermodynamic properties are often given by a very complex database, however, solving the EDP condition can substantially limit the computational efficiency of the PFMs. In this study, we present a method to effectively solve the EDP condition. By modifying the PFM with finite interface dissipation, a relaxation equation for the partition coefficient is extracted. We adopt this relaxation equation to replace the EDP condition in a conventional PFM. This relaxation equation is straightforwardly extended to a multicomponent and multiphase system. The relaxation equation for dilute ideal alloys appears to be fully independent of the phase field and the diffusion field, so it can be analytically solved. We obtain a criterion for the relaxation parameter to effectively maintain the EDP condition in the interfacial region. Using the PFM coupled with the relaxation equation, we simulate the dendritic growth in an Al-Si alloy with a full thermodynamic database and compare the results with the predictions obtained from the relaxation equation. The relaxation kinetics in the simulations are in excellent agreement with the predictions. We apply the present PFM to simulate the microstructure evolution for early stage solidification during continuous casting of a quaternary steel alloy under real process conditions. We systemically examine the effects of the relaxation parameter. The present criterion for the choice of the relaxation parameter can be used for multicomponent nondilute alloys.