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On equilibrium two-phase microstructures at plane strain

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Abstract

Stress-induced phase transformations in linear elastic solids are considered for the case of plane strain on the basis of a previously developed procedure that includes finding the optimal composite microstructures which provide the exact lower bound of the energy and the equilibrium new phase volume fraction that satisfies the thermodynamic equilibrium condition. Stress–strain diagrams are constructed for various deformation paths on which phase transformations are controlled by average strains or by different components of average strain and average stresses. Strain hardening and strain softening effects are demonstrated on the path of the transformation. In the case of mixed strain-stress control, regimes for which the minimizing volume fraction does not correspond to any optimal microstructure, or optimal microstructures which could not satisfy the thermodynamic equilibrium condition with respect to the new phase volume fraction, are presented. It is shown that this leads to the incompleteness of a gradual phase transformation, jump-like transformation behavior, and jump in stress. An indifferent equilibrium regime is also discussed.

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Acknowledgements

The financial support from the Russian Science Foundation (Grant No. 19-19-00552) is greatly appreciated.

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Authors and Affiliations

  1. Institute for Problems in Mechanical Engineering of Russian Academy of Sciences, 61, Bolshoy pr. V. O., St., Petersburg, Russia, 199178

    Alexander B. Freidin & Leah L. Sharipova

  2. Peter the Great St. Petersburg Polytechnic University, 29, Politechnicheskaya str., St, Petersburg, Russia, 195251

    Alexander B. Freidin

  3. St. Petersburg University, Universitetsky Pr. 28, Peterhof, Russia, 198504

    Alexander B. Freidin

  4. University of Utah, 155 S 1400 E, Salt Lake City, UT, 84112, USA

    Andrej V. Cherkaev

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  1. Alexander B. Freidin
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  2. Leah L. Sharipova
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  3. Andrej V. Cherkaev
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Correspondence to Alexander B. Freidin.

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Freidin, A.B., Sharipova, L.L. & Cherkaev, A.V. On equilibrium two-phase microstructures at plane strain. Acta Mech 232, 2005–2021 (2021). https://doi.org/10.1007/s00707-020-02905-2

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  • DOI: https://doi.org/10.1007/s00707-020-02905-2

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