Numerical simulation of microstructural evolution of inhomogeneous elastic media

We develop a new diffuse interface model for studying morphology of precipitate during the evolution of inhomogeneous elastic media (binary alloys) in two and three dimensions. In this model, evolution is occurred by lowering the generalized Cahn-Hilliard free energy. Many researchers have acknowledged that elasticity plays an important role in microstructural evolution of binary alloys. We carefully implemented elasticity to the model and it is solved by preconditioned conjugate gradient method. A pseudo spectral method is used to solve the diffuse interface system. By linear analysis, we show linear stability of the numerical method.; Through numerical simulations, we show that the new model captures accurate morphology of precipitate. One particle evolution shows a good agreement with the three-dimensional results of Mueller et al. [16][17], and Thompson and Voorhees [38], such as transitions from spheres to convex or concave cuboids. Merging of two particles is studied including the required conditions, and the velocity of merging depending on softness of materials and initial placements. Plate structures are observed for two soft particles placed on <110> directions and four particles placed on the z = 0 plane. These studies confirm the importance of elasticity in microstructural evolution of elastically stressed binary alloys.