Chemo-mechanical benchmark for phase-field approaches

Modelling and Simulation in Materials Science and Engineering, vol. 33, pp. 015004

Abstract

Abstract Phase-field approaches have gained increasing popularity as a consequence of their ability to model complex coupled multi-physical problems. The efficient modeling of migrating diffuse phase boundaries is a fundamental characteristic. A notable advantage of phase-field methods is their ability to account for diverse physical driving forces for interfacial motion due to diffusive, mechanical, electro-chemical, and other processes. As a result of this versatility, phase-field methods are frequently employed in the fields of materials science, mechanics, and physics, and are continually undergoing development. To test the accuracy of these developments, it is indispensable to establish standardized benchmark tests, to ensure the thermodynamic consistency of studies carried out. This work presents a series of such tests based on chemo-elastic equilibrium states for Fe-C binary alloys, benchmarking the performance of a phase-field model with chemo-elastic coupling based on the grand potential density. Use of parameters for the Fe-C system from a Calphad database allows for the determination of the Gibbs free energy, thereby enabling the quantification of chemical driving forces. For a circular inclusion, the capillary driving force is derived on a geometrically motivated basis using the lever rule and expressed as a function of the chemical potential. These simulations contribute to the development of standardized benchmark tests that validate chemical, capillary, and mechanical driving forces separately and in combination. The present study compares phase-field simulation results with results from the analytic solution of chemo-elastic boundary value problems and the generalized Gibbs–Thomson equation.

Authors 5

1. Thea Kannenberg

   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, 76131 Karlsruhe, Germany

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

2. Andreas Prahs

   Karlsruhe Institute of Technology

   Affiliation as printed

   Karlsruhe Institute of Technology (KIT), Institute for Applied Materials (IAM-MMS), Straße am Forum 7, 76131 Karlsruhe, 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, 40237 Düsseldorf, Germany

   RWTH Aachen University, Material Mechanics, Schinkelstraße 2, 52062 Aachen, 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, 76131 Karlsruhe, Germany

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

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

5. Daniel Schneider

   Karlsruhe Institute of Technology · Karlsruhe University of Applied Sciences

   Affiliation as printed

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

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