An efficient and quantitative phase-field model for elastically heterogeneous two-phase solids based on a partial rank-one homogenization scheme

This paper presents an efficient and quantitative phase-field model for elastically heterogeneous alloys that ensures the two mechanical compatibilities$\unicode{x2014}$static and kinematic, in conjunction with chemical equilibrium within the interfacial region. Our model contrasts with existing phase-field models that either violate static compatibility or interfacial chemical equilibrium or are computationally costly. For computational efficiency, the partial rank-one homogenization (PRH) scheme is employed to enforce both static and kinematic compatibilities at the interface. Moreover, interfacial chemical equilibrium is ensured by replacing the composition field with the diffusion potential field as the independent variable of the model. Its performance is demonstrated by simulating four single-particle and one multi-particle cases for two binary two-phase alloys: Ni-Al $\gamma^{\prime}/\gamma$ and UO$_2$/void. Its accuracy is then investigated against analytical solutions. For the single-particle $\gamma^{\prime}/\gamma$ alloy, we find that the accuracy of the phase-field results remains unaffected for both planar and non-planar geometries when the PRH scheme is employed. Fortuitously, in the UO$_2$/void simulations, despite a strong elastic heterogeneity$\unicode{x2014}$the ratio of Young's modulus of the void phase to that of the UO$_2$ phase is $10^{-4}\unicode{x2014}$we find that the PRH scheme shows significantly better convergence compared to the Voigt-Taylor scheme (VTS) for both planar and non-planar geometries. Nevertheless, for the same interface width range as in the $\gamma^{'}/\gamma$ case, the interface migration in these simulations shows dependence on interface width. Contrary to the $\gamma^{\prime}/\gamma$ simulations, we also find that the simulated elastic fields show deviations from the analytical solution in the non-planar UO$_2$/void case using the PRH scheme.