Numerical benchmark of phase-field simulations with elastic strains: Precipitation in the presence of chemo-mechanical coupling
R. Darvishi Kamachali, C. Schwarze, M. Lin, M. Diehl , P. Shanthraj, U. Prahl, I. Steinbach, D. Raabe.
Phase-field studies of solid-state precipitation under strong chemo-mechanical coupling are performed and benchmarked against the existing analytical solutions. The open source software packages OpenPhase and DAMASK are used for the numerical studies. Solutions for chemical diffusion and static mechanical equilibrium are investigated individually followed by a chemo-mechanical coupling effect arising due to composition dependence of the elastic constants. The accuracy of the numerical solutions versus the analytical solutions is quantitatively discussed. For the chemical diffusion benchmark, an excellent match, with a deviation <0.1%, was obtained. For the static mechanical equilibrium benchmark Eshelby problem was considered where a deviation of 5% was observed in the normal component of the stress, while the results from the diffuse interface (OpenPhase) and sharp interface (DAMASK) models were slightly different. In the presence of the chemo-mechanical coupling, the concentration field around a static precipitate was benchmarked for different coupling coefficients. In this case, it is found that the deviation increases proportional to the coupling coefficient that represents the strength of coupling concentration and elastic constants. Finally, the interface kinetics in the presence of the considered chemo-mechanical coupling were studied using OpenPhase and a hybrid OpenPhase–DAMASK implementation, replacing the mechanical solver of OpenPhase with DAMASK’s. The observed deviations in the benchmark studies are discussed to provide guidance for the use of these results in studying further phase transformation models and implementations involving diffusion, elasticity and chemo-mechanical coupling effect.
Stress distribution in the Eshelby benchmark test against the analytical solution with different softwares. Left: Stress distribution perpendicular to the cross section in colour. Right: Normal and tangential stress in radial direction.