Modeling precipitate growth in multicomponent alloy systems by a variational principle

Abstract

A physically based state variable model is proposed to simulate precipitate growth encountered in many industry-relevant precipitation processes. The model is derived from the same variational principle used in deriving the phase field method, and is able to efficiently model diffusion-controlled precipitate growth in multicomponent alloy systems. One of the new features of the model is its treatment of the propagation of the diffusion boundary layer surrounding a growing precipitate. The model was applied to simulate spherical precipitate growth in Al–Mg–Si, Ni–Al–Ti and Fe–C alloy systems, and the simulation results were verified by a direct detailed finite volume-based approach. Compared with the approximate growth models that have been reported, e.g., the invariant field model, the SFFK model and the model by Chen et al., the proposed model’s predictions are much closer to the direct detailed approach, especially for growth under high supersaturation conditions. It is concluded that the proposed model is valuable and could be embedded into a multiscale modeling framework to deal with concurrent nucleation, growth, coarsening and macroscopic transportation. This work is also a successful case study demonstrating the potential offered by the variational principle for multiscale microstructural evolution modeling.