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Generalized von Mises Criterion as a Tool for Determining the Strength Properties of Hexagonal Materials


Using the previously proposed generalization of the von Mises yield criterion for crystals with a hexagonal lattice, the dependence of the stress tensor on the strain tensor and applied external pressure is found. The case of plane deformation with an arbitrary orientation of crystallites is analyzed in detail. The components of the stress tensor deviator for magnesium single crystals with all kinds of orientations are calculated, and the stress level lines are plotted for the onset of plastic flow.

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  1. A. M. Vlasova and A. G. Kesarev, “Deformation model of magnesium single crystals,” Russ. Phys. J. 61, No. 7, 1258–1269 (2018).

    CAS  Article  Google Scholar 

  2. A. M. Vlasova and A. G. Kesarev, “A generalization of the von mises criterion for a single crystal with a hexagonal crystal lattice,” Mech. Solids. 54, 1197–1207 (2019).

    Article  Google Scholar 

  3. B. E. Pobedrya, Mechanics of Composites (Izdatel’stvo Moskovskogo Universiteta, Moscow, 1984).

    Google Scholar 

  4. P. V. Trusov, P. S. Volegov, and N. S. Kondrat’ev, Physical Theory of Plasticity (Izd-vo Permskogo natsional’nogo issledovatel’skogo politekhnicheskogo un-ta, Perm, 2013) [in Russian].

  5. L. I. Sedov, Continuum Mechanics (Nauka, Moscow, 1994), Vol. 2 [in Russian].

    Google Scholar 

  6. L. I. Sedov, Continuum Mechanics (Nauka, Moscow, 1994), Vol. 1 [in Russian].

    Google Scholar 

  7. B. E. Pobedrya, Lectures on Tensor Analysis (Izdatel’stvo Moskovskogo Universiteta, Moscow, 1986).

    Google Scholar 

  8. E. W. Kelly and W. F. Hosford, “Plane-strain compression of magnesium and magnesium alloy crystals,” Trans. Metall. Soc. AIME 242, 5–15 (1968).

    Google Scholar 

  9. B. C. Wonsiewicz and W. A. Backofen, “Plasticity of magnesium crystals,” Trans. AIME 239, 1422–1431 (1967).

    CAS  Google Scholar 

  10. Ya. S. Umanskii, Yu. A. Skakov, A. M. Ivanov, and L. I. Rastorguev, Crystallography, X-ray Diffraction, and Electron Microscopy (Metallurgiya, Moscow, 1982).

    Google Scholar 

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The study was conducted within the framework of State assignment no. AAAA-A18-118020190104-3 on topic Pressure.

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Correspondence to A. M. Vlasova.

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The authors declare that they have no conflicts of interest.

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Translated by O. Kadkin

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Kesarev, A.G., Vlasova, A.M. Generalized von Mises Criterion as a Tool for Determining the Strength Properties of Hexagonal Materials. Phys. Metals Metallogr. 123, 186–192 (2022).

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  • magnesium
  • deformation
  • hexagonal crystals
  • strength
  • yield criterion