Study of Martensitic Phase Transformation in Silicon and Zirconium Using Scale-Free Phase-Field Model

ORAL

Abstract

Silicon undergoes a martensitic phase transformation from cubic Si I to tetragonal Si II with large and very anisotropic transformation strain, whereas zirconium transforms from hcp α – phase to simple hexagonal ω – phase under high pressure. Scale-free phase-field model for phase transformations at large strains is advanced and used to study the multivariant high-pressure phase transformations in Si and Zr under various nonhydrostatic loadings. The phase field model is implemented using finite element algorithms in deal.II. The model is calibrated using available experimental and atomistic data. It is applied to study forward and reverse phase transformations in single and polycrystal Si and Zr crystals under different non-hydrostatic conditions and varying strain rates. The mesh size is also varied to study the microstructure evolution in detail. The single crystal results were used to validate the model and the parameters with analytical results. The validated model was then used to study texture free polycrystal samples generated using DREAM.3D. Also, fields of all components of the stress and transformation strain tensors, volume fractions of martensitic variants and high-pressure phase, and macroscopic strain-strain and volume fractions strain plot are presented. The developed methodology can be used for studying similar PTs with large transformation strains and for further development by including plastic strain and strain-induced phase transformations.

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Publication: 1. Babaei H., Levitas V.I. Finite-strain scale-free phase-field approach to multivariant martensitic phase transformations with stress-dependent effective thresholds. J. Mech. Physics Solids, 2020, 144, 104114.
2. Pandey K. K., Levitas V. I. In situ quantitative study of plastic strain-induced phase transformations under high pressure: Example for ultra-pure Zr. Acta Materialia, 2020, 196, 338-346.
3. Levitas V.I., Chen H., Xiong L. Lattice instability during phase transformations under multiaxial stress: modified transformation work criterion. Phys. Rev. B, 96, 054118 (2017).
4. Zarkevich N. A., Chen H., Levitas V.I., and Johnson D. D. Lattice instability during solid-solid structural transformations under general applied stress tensor: example of Si I?Si II with metallization. Phys. Rev. Lett., 121, 165701 (2018).
5. Chen H., Zarkevich N. A., Levitas V. I., Johnson D. D., and Zhang X. Fifth-degree elastic energy for predictive continuum stress-strain relations and elastic instabilities under large strain and complex loading in silicon. NPJ Computational Materials. (2020) 6, 115.
6. Levitas V.I., Esfahani S.E., and Ghamarian I. Scale-free modeling of coupled evolution of discrete dislocation bands and multivariant martensitic microstructure. Phys. Review Lett., 121, 20570 (2018).
7. Esfahani S.E., Ghamarian I., Levitas V.I. Strain-induced multivariant martensitic transformations: A scale-independent simulation of interaction between localized shear bands and microstructure. Acta Materialia, 2020, 196, 430-443.

Presenters

  • Raghunandan Pratoori

    Iowa State University

Authors

  • Raghunandan Pratoori

    Iowa State University

  • Hamed Babaei

    Iowa State University

  • Valery I Levitas

    Iowa State University