Effects of internal stresses and intermediate phases on the coarsening of coherent precipitates: A phase-field study

Phase stability, topology and size evolution of precipitates are important factors in determining the mechanical properties of crystalline materials. In this article, the Cahn-Hilliard type of phase-field model was coupled to elasticity equations within a mixed-order Galerkin finite element framework to study the coarsening morphology of coherent precipitates. The effects of capillarity, particle size and fraction, compositional strain, and inhomogeneous elasticity on the kinetics and kinematics of coherent precipitates in a binary dual phase crystal admitting a third intermediate stable/meta-stable phase were investigated. The results demonstrated the ability of the model to simulate coarsening under the concomitant action of Ostwald ripening and mismatch elastic strain mechanisms. Using a phenomenological coarsening power law, coarsening rates were determined to depend on precipitate size and volume fraction, compositional strain, and strain mismatch between precipitates and the matrix. Results also showed that the necking incubation time between two neighboring precipitates depends inversely on the precipitate's initial sizes; however, under fixed volume fraction of precipitates, any increase in the initial sizes of the precipitates mitigates the coarsening. Meanwhile, the compositional strain and the growth of the intermediate stable/meta-stable phase leads to substantial enhancements of precipitate coarsening.