Coupling approaches in chemo-mechanical multiphase-field models

International Journal of Mechanical Sciences, vol. 303, pp. 110569

Abstract

Owing to their ability to combine various driving forces and their numerically efficient handling of migrating interfaces, multiphase-field models are widely employed in the multiphysics-based modeling and simulation of multiphase systems in materials science. Chemo-mechanically coupled phenomena, such as stress-driven diffusion and diffusion-induced stresses, are of high interest in various fields including battery materials research and metals. This work discusses the impact of the chemo-mechanical coupling approach on equilibrium states, phase evolution, and component diffusion. To this end, a fully coupled multiphase-field model is derived that accounts for balance equations on singular surfaces and the Hadamard jump conditions. Consequently, mechanical compatibility and chemical equilibrium are ensured in both bulk and interface regions. Furthermore, a scheme is presented that facilitates a direct comparison of the chemo-mechanically fully coupled model with a one-sided and a weakly coupled model. The proposed scheme enables a comparison with sharp interface calculations that are derived from the generalized Gibbs-Thomson equation. Additionally, this scheme is employed as a benchmark to validate the proposed model. Moreover, it is demonstrated that only a model that employs a full chemo-mechanical coupling is capable of capturing stress-driven diffusion as well as diffusion-induced stress. • A chemo-mechanically fully coupled multiphase-field method is derived. • Balance equations at singular surfaces are considered within diffuse interfaces. • A comparison scheme for chemo-mechanical coupling approaches is proposed. • The coupling impacts diffusion, microstructure evolution, and equilibrium states. • A benchmark with analytical sharp interface solutions is derived to validate coupled phase-field models.

Authors 5

1. Thea Kannenberg corresponding

   Karlsruhe Institute of Technology · Karlsruhe University of Applied Sciences

   Affiliation as printed

   Karlsruhe Institute of Technology (KIT), Institute for Applied Materials (IAM-MMS), Straße am Forum 7, Karlsruhe, 76131, Germany

   Karlsruhe University of Applied Sciences, Institute of Digital Materials Science (IDM), Moltkestraße 30, Karlsruhe, 76133, Germany

2. Andreas Prahs

   Karlsruhe Institute of Technology

   Affiliation as printed

   Karlsruhe Institute of Technology (KIT), Institute of Nanotechnology (INT-MSS), Hermann-von-Helmholtz-Platz 1, Eggenstein-Leopoldshafen, 76344, Germany

3. Bob Svendsen Aachen

   Max-Planck-Institut für Nachhaltige Materialien · RWTH Aachen University

   Affiliation as printed

   Max Planck Institute for Sustainable Materials, Microstructure Physics and Alloy Design, Max–Planck-Straße 1, Düsseldorf, 40237, Germany

   RWTH Aachen University, Material Mechanics, Schinkelstraße 2, Aachen, 52062, Germany

4. Britta Nestler

   Karlsruhe Institute of Technology · Karlsruhe University of Applied Sciences

   Affiliation as printed

   Karlsruhe Institute of Technology (KIT), Institute for Applied Materials (IAM-MMS), Straße am Forum 7, Karlsruhe, 76131, Germany

   Karlsruhe Institute of Technology (KIT), Institute of Nanotechnology (INT-MSS), Hermann-von-Helmholtz-Platz 1, Eggenstein-Leopoldshafen, 76344, Germany

   Karlsruhe University of Applied Sciences, Institute of Digital Materials Science (IDM), Moltkestraße 30, Karlsruhe, 76133, Germany

5. Daniel Schneider

   Karlsruhe Institute of Technology · Karlsruhe University of Applied Sciences

   Affiliation as printed

   Karlsruhe Institute of Technology (KIT), Institute for Applied Materials (IAM-MMS), Straße am Forum 7, Karlsruhe, 76131, Germany

   Karlsruhe University of Applied Sciences, Institute of Digital Materials Science (IDM), Moltkestraße 30, Karlsruhe, 76133, Germany