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

Lin, Yueh-Yu; Schleifer, Felix; Holzinger, Markus; Ta, Na; Skrotzki, Birgit; Kamachali, Reza Darvishi; Glatzel, Uwe; Fleck, Michael

doi:10.3390/ma14061373

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

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Ta, Na
Theory and Simulation, Microstructure Physics and Alloy Design, Max-Planck-Institut für Eisenforschung GmbH, Max Planck Society;
School of Material Science and Engineering, University of Science & Technology Beijing, Beijing 100083, China;

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Kamachali, Reza Darvishi
Theory and Simulation, Microstructure Physics and Alloy Design, Max-Planck-Institut für Eisenforschung GmbH, Max Planck Society;
Federal Institute for Materials Research and Testing (BAM), Unter den Eichen 87, 12205, Berlin, Germany;

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Citation

Lin, Y.-Y., Schleifer, F., Holzinger, M., Ta, N., Skrotzki, B., Kamachali, R. D., et al. (2021). Quantitative Shape-Classification of Misfitting Precipitates during Cubic to Tetragonal Transformations: Phase-Field Simulations and Experiments. Materials, 14(6): 1373. doi:10.3390/ma14061373.

Cite as: https://hdl.handle.net/21.11116/0000-0009-71AC-6

Abstract

The effectiveness of the mechanism of precipitation strengthening in metallic alloys de-pends on the shapes of the precipitates. Two different material systems are considered: tetragonal γ′′ precipitates in Ni-based alloys and tetragonal θ′ precipitates in Al-Cu-alloys. The shape formation and evolution of the tetragonally misfitting precipitates was investigated by means of experiments and phase-field simulations. We employed the method of invariant moments for the consistent shape quantification of precipitates obtained from the simulation as well as those obtained from the experiment. Two well-defined shape-quantities are proposed: (i) a generalized measure for the particles aspect ratio and (ii) the normalized λ2, as a measure for shape deviations from an ideal ellipse of the given aspect ratio. Considering the size dependence of the aspect ratio of γ′′ precipitates, we find good agreement between the simulation results and the experiment. Further, the precipitates’ in-plane shape is defined as the central 2D cut through the 3D particle in a plane normal to the tetragonal c-axes of the precipitate. The experimentally observed in-plane shapes of γ′′-precipitates can be quantitatively reproduced by the phase-field model. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.