Abstract
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.
Similar content being viewed by others
REFERENCES
A. M. Vlasova and A. G. Kesarev, “Deformation model of magnesium single crystals,” Russ. Phys. J. 61, No. 7, 1258–1269 (2018).
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).
B. E. Pobedrya, Mechanics of Composites (Izdatel’stvo Moskovskogo Universiteta, Moscow, 1984).
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].
L. I. Sedov, Continuum Mechanics (Nauka, Moscow, 1994), Vol. 2 [in Russian].
L. I. Sedov, Continuum Mechanics (Nauka, Moscow, 1994), Vol. 1 [in Russian].
B. E. Pobedrya, Lectures on Tensor Analysis (Izdatel’stvo Moskovskogo Universiteta, Moscow, 1986).
E. W. Kelly and W. F. Hosford, “Plane-strain compression of magnesium and magnesium alloy crystals,” Trans. Metall. Soc. AIME 242, 5–15 (1968).
B. C. Wonsiewicz and W. A. Backofen, “Plasticity of magnesium crystals,” Trans. AIME 239, 1422–1431 (1967).
Ya. S. Umanskii, Yu. A. Skakov, A. M. Ivanov, and L. I. Rastorguev, Crystallography, X-ray Diffraction, and Electron Microscopy (Metallurgiya, Moscow, 1982).
Funding
The study was conducted within the framework of State assignment no. AAAA-A18-118020190104-3 on topic Pressure.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare that they have no conflicts of interest.
Additional information
Translated by O. Kadkin
Rights and permissions
About this article
Cite this article
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). https://doi.org/10.1134/S0031918X22020041
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0031918X22020041