Comparison of excess free energy at an interface according to the applied interpolation scheme for elasticity: A phase-field method

• Published in: Computational materials science Vol. 243; p. 113111
• Main Authors: Shin, Wooseob, Simon, Pierre-Clément A., Chang, Kunok
• Format: Journal Article
• Language: English
• Published: United States Elsevier B.V 01.07.2024; Elsevier
• Subjects: Elasticity; Interface energy; Interpolation schemes; MATERIALS SCIENCE; Microstructure evolution modeling; Phase field model; Phase field model; Elasticity; Interpolation schemes; Interface energy; Microstructure evolution modeling
• ISSN: 0927-0256; 1879-0801
• DOI: 10.1016/j.commatsci.2024.113111

Phase-field modeling is an effective simulation technique for modeling microstructure evolution of elastically anisotropic systems. To introduce the elastic energy contribution in a phase field model, an interpolation scheme is used to define the mechanical properties within the phases and across the continuous interface. Several existing interpolation schemes introduce a potential excess elastic energy at the interface, which undesirable effect on microstructure evolution needs to be evaluated. In this study, we focused on three interpolation schemes including Khachaturyan’ scheme (KHS), Voigt–Taylor’s scheme (VTS), and Steinbach–Apel’s scheme (SAS). Comparisons of these schemes’ performances were performed in three configuration types using the MOOSE (Multiphysics Object-Oriented Simulation Environment) framework: bi-crystal, isotropic particle-matrix and anisotropic particle-matrix. The contribution of excess elastic energy on the interface energy as a function of interface width and the computational time to steady-state were evaluated in these three configurations. SAS introduces the lowest excess elastic energy contribution and the VTS has the biggest contribution amongst the considered schemes. Moreover, when modeling precipitation in an anisotropic elastic material, the SAS approach seems to predict more physical convex shapes during growth, making it preferable to KHS and VTS. As currently implemented, SAS requires the largest computational time and KHS requires the smallest time to reach steady-state amongst the considered schemes. [Display omitted]