Multiscale, Coupled Chemo-mechanical Modeling of Bainitic Transformation During Press Hardening

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

“…In the hybrid implementation, we utilize the DAMASK for solving static mechanical equilibrium (Equation (5)) and the OpenPhase finite difference solver for homogenization and solving the diffusion and phasefield equations. While in OpenPhase an elastic spectral solver suited for small deformations is implemented, the spectral solver in DAMASK is based on the finite strain framework [74,72,73] that makes it suited for studying large deformations as presented in [75,53]. It calculates the solution of all 9 components of the deformation gradient F ij to the static equilibrium equation…”

“…composition dependence of elastic constants, was indeed discovered long ago [51] but neglected until recently when its effect on the equilibrium concentration profile around a precipitate has been discussed [52] and applied for studying precipitation in NiTi shape memory alloys [27]. Similar coupling effects manifest themselves in different processes such as bainitic transformation [53], adsorption [54] and shape memory effects [27,55]. Currently, chemo-mechanical coupling effects in metals and polymers are the subject of the priority research programme, SPP1713 [56], initiated by the German Research Foundation (DFG).…”

Modeling Bainitic Transformations during Press Hardening

“…At this length scale, a coarse grained representation of the bainitic ferrite sheaves is necessary for the balance between representative volume element (RVE) size and computational costs of the model. Therefore, in [ 74 , 75 , 76 ], we have described every bainitic packet (sheaves of the same close-packed group) by individual order parameters. The mechanical and chemical driving forces are derived as variational derivative of the free energy functional.…”

“…Using the multi-phase-field framework of Steinbach et al [ 77 ], different interfacial properties can be assigned to the austenite-austenite grain boundaries, austenite-packet boundaries and the inter-packet boundaries. In [ 74 , 76 ], phase field simulations have been coupled with a finite element simulation on the macroscopic scale. For each integration point of the finite elements, an individual phase field simulation domain is created, where the stress tensor of the integration point is incrementally applied to the phase field simulation.…”

“…The simulation can reproduce the overall transformation induced strain and the effect of variant selection on bainitic packets. For further details of the simulation approach and results, we refer to [ 74 ].…”