Numerical Benchmark of Phase-Field Simulations with Elastic Strains: Precipitation in the Presence of Chemo-Mechanical Coupling

Abstract

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. In this case, 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 chemomechanical coupling, the concentration field around a static precipitate was benchmarked for different coupling coefficients that represent the strength of composition dependency of elastic constants. It is found that the deviation increases proportional to the coupling coefficient. 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.

Modeling Bainitic Transformations during Press Hardening

“…We have compared results from the following three numerical combinations: OpenPhase only, DAMASK only and the OpenPhase chemical solver coupled with the DAMASK mechanical solver. All numerical results agree well with each other with a mean deviation of around 5% (for the concentration field including the diffusive interface area) [97].…”

Solving Material Mechanics and Multiphysics Problems of Metals with Complex Microstructures Using DAMASK—The Düsseldorf Advanced Material Simulation Kit

“…In this overview article published on the occasion of AEM 's 20th anniversary, we present recent application examples showing how DAMASK can be used to investigate the response of metallic microstructures to applied loads. While, due to DAMASKs origin as a crystal plasticity framework, most examples presented here deal with the materials response to mechanical loads, they also demonstrate—along with several recent publications—its capabilities as a multiphysics ICME tool. The examples presented here are mainly based on existing publications and include yield‐surface‐based forming simulations, Lankford value predictions, and the forecast of damage in multiphase steels.…”

Simulation of the θ′ Precipitation Process with Interfacial Anisotropy Effects in Al-Cu Alloys

“…A multi-phase-field (MPF) model is used through the open-source microstructure simulation package OpenPhase [ 39 , 40 ]. On a given volume Ω , a general free energy density can be split into interfacial , chemical and elastic contributions [ 41 , 42 , 43 , 44 ], where N is the local number of phases and the sum constraint is everywhere fulfilled.…”

“… is the diffusion potential of component i in phase α. The chemo-mechanical effects were introduced by considering a linear composition dependence of elastic constants as detailed in [ 10 , 39 ].…”