Phase-field modeling of γ/γ″ microstructure formation in Ni-based superalloys with high γ″ volume fraction

Abstract

The excellent mechanical properties of the Ni-based superalloy IN718 mainly result from coherent γ precipitates. Due to a strongly anisotropic lattice misfit between the matrix and the precipitate phase, the particles exhibit pronounced plate-shaped morphologies. Using a phase-field model, we investigate various influencing factors that determine the equilibrium shapes of γ precipitates, minimizing the sum of the total elastic and interfacial energy. Upon increasing precipitate phase fractions, the model predicts increasingly stronger particle-particle interactions, leading to shapes with significantly increased aspect ratios. Matching the a priori unknown interfacial energy density to fit experimental γ shapes is sensitive to the phase content imposed in the underlying model. Considering vanishing phase content leads to 30 % lower estimates of the interfacial energy density, as compared to estimates based on realistic phase fractions of 12 %. We consider the periodic arrangement of precipitates in different hexagonal and rectangular superstructures, which result from distinct choices of point-symmetric and periodic boundary conditions. Further, non-volume conserving boundary conditions are implemented to compensate for strains due to an anisotropic lattice mismatch between the γ matrix and the γ precipitate. As compared to conventional boundary conditions, this specifically tailored simulation configuration does not conflict with the systems periodicity and provides substantially more realistic total elastic energies at high precipitate volume fractions. The energetically most favorable superstructure is found to be a hexagonal precipitate arrangement.c 2020. The manuscript is made available under the license CC-BY-NC-ND 4.0

Quantitative Shape-Classification of Misfitting Precipitates during Cubic to Tetragonal Transformations: Phase-Field Simulations and Experiments

“…With respect to the boundaries, we apply periodic boundary conditions for all fields. To account for volume change of the simulation domain, we apply non-volume-conserving boundary conditions [ 5 ].…”

“…Diffusivities of the individual alloying elements are taken from the Dictra database MOBNi4. The interfacial energy is assumed to be isotropic and is estimated from ripening data and from the size dependent aspect ratio of the precipitates respectively [ 5 , 35 , 36 , 37 ].…”

“…The large misfit was found to be in the order of −5 × 10 −3 [ 7 , 46 ] while the absolute value of the smaller misfit is a factor of 10 smaller. In the case of such a strong tetragonal anisotropy of the misfit, the precipitate aspect ratio only depends on the larger misfit [ 5 ].…”

“…In this work, we consider two different technologically successful materials with certain common aspects in their precipitation microstructure: (i) the precipitation of the tetragonal γ″ phase (Ni 3 Nb) in Nb-containing Ni-based alloys [ 5 , 6 ] and (ii) the precipitation of the tetragonal θ′ phase (Al 2 Cu) in Al-Cu alloys [ 7 , 8 ]. Both cases involve cubic to tetragonal transformations with a strongly anisotropic lattice misfit, where the misfit, ε 3 , in the tetragonal c-axes is about an order of magnitude larger than the misfit, ε 1 , in the other two basic lattice directions.…”

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

“…Mesoscale approaches may seem more appealing to achieve larger length and time scales [ 34 , 35 ]. The meso-scale phase-field approach has also recently been employed to simulate shape formation of plate-like precipitates [ 36 ]. Li and Chen [ 37 ] simulated stress-oriented nucleation and growth of θ′ precipitates using two parabolic functions to describe the chemical free energies for the θ′- and α-phases.…”