Multi-scale modeling of the complex microstructural evolution in structural phase transformations

Modeling the microstructural evolution in structural phase transformations remains challenging, mostly due to the competitions among the potential product phases and the multi-scale nature. To develop a practical tool for such a scientifically and technologically important issue, a multi-scale framework is proposed, where a coarse graining scheme based on the probability density distribution of the representative volume elements (RVEs) of product phases is coupled with the maximal entropy production principle (MEPP) to model the competitions among the multiple product phases as the selection of dissipative paths, and a Fokker-Planck type equation is obtained for the evolution of multiple microstructural parameters (MPs) for the product phases. Applied to precipitation in Al-Cu alloys, the present model, free of adjustable parameters, predicts a correct sequence of precipitation, i.e. GP zone → θꞌꞌ → θꞌ and yields the accurate precipitation kinetics for θꞌꞌ and θꞌ as compared with the previous experimental data, thus demonstrating the inherent correlation between the MPs and thermodynamics and kinetics of the transformation. For the complex transformations in engineering alloys, the current framework, starting from the general statistical principles and the MEPP, can incorporate the specific MPs for a given transformation following the same scheme.