Chemo-elastic benchmark for a multiphase-field model
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Multiphase-field models are a well-established method for the simulation of phase transformation processes in materials science. The migration of the diffuse phase boundaries, present in a multiphase-field method, can be efficiently simulated without the need of numerically expensive tracking. A chemo-elastically coupled multiphase-field model is employed [5]. Herein, chemical driving forces based on the grand potential density [1, 3] and mechanical driving forces based on the mechanical jump conditions [4] recover sharp interface solutions. Thermodynamic and mechanical equilibrium conditions are given by the sharp interface formulation. An interfacial equilibrium condition is given by the Gibbs-Thomson equation [2]. Parameters from a CALPHAD-database are incorporated to approximate the Gibbs free energy with parabolic functions and, thus, quantify the chemical driving forces. This work discusses a series of phase equilibrium simulations of Fe-C binary alloys, which contribute to the development of standard benchmark examples to validate chemical, capillary, and mechanical driving forces. Analytical solutions are derived and compared with phase-field simulations. References [1] A. Choudhury and B. Nestler, Phys Rev E, Vol. 85 (2), 021602, 2012. [2] W.C. Johnson and J.I.D. Alexander, J Appl Phys, Vol. 59 (8), 2735–2746, 1986. [3] M. Plapp, Phys Rev E, Vol. 84 (3), 031601, 2011. [4] D. Schneider, F. Schwab. E. Schoof, A. Reiter, C. Herrmann, M. Selzer, T. Böhlke and B. Nestler, Comput Mech, Vol. 60 (2), 203–217, 2017. [5] B. Svendsen, P. Shanthraj and D. Raabe, J Mech and Phys Solids, Vol. 112, 619–636, 2018.
