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New Discrete Model of Plastic Deformation of Solid Bodies

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Materials Science Aims and scope

We compare the dislocation model with a new discrete model of plasticity. According to the previously proposed model, a crystal lattice with spherically symmetric potential of interatomic interaction is unstable under shear stresses in the internal regions of the crystal. The surface layers preserve the unstable crystal lattice, which creates the state of unstable equilibrium in the crystal. As an important feature of the proposed model, we can mention the fact that the shift of atomic planes in the crystal occurs under low stresses in the absence of any defects, including dislocations. We also describe the advantages of the proposed model as compared with the dislocation model discovered in the course of analysis of the available experimental data.

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References

  1. L. Yu. Kozak, “Plasticity and instability of crystal lattices,” Metalofiz. Noveish. Tekhnol.,34, No. 5, 1529−1545 (2012).

    CAS  Google Scholar 

  2. L. Kozak, “New atomic model of metals plastic deformation,” ASCIT J. Mater.,3, No. 5, 26–32 (2017); http://www.aascit.org/journal/archive?journalId=974&issueId=9740305.

    Google Scholar 

  3. L. Y. Kozak, “Investigation of the instability of crystal lattice by using discrete models,” Fiz.-Khim. Mekh. Mater.,53, No. 3, 118−123 (2017); English translation:Mater. Sci.,53, No. 3, 424−430 (2017); https://doi.org/https://doi.org/10.1007/s11003-017-0091-x).

  4. L. Yu. Kozak, “Discrete models of plastic deformation of solids under the action of high hydrostatic pressure,” Fiz.-Khim. Mekh. Mater.,52, No. 1, 98−101 (2016); English translation:Mater. Sci.,52, No. 1, 108–112 (2016).

  5. L. Yu. Kozak, “Discrete models of martensitic transformation and twinning in metals,” Fiz.-Khim. Mekh. Mater.,48, No. 5, 83−87 (2012); English translation:Mater. Sci.,48, No. 5, 647–652 (2013); https://doi.org/https://doi.org/10.1007/s11003-013-9550-1).

  6. M. V. Klassen-Neklyudova and T. A. Kontorova, “On the dislocation hypothesis of plasticity,” Usp. Fiz. Nauk,11, No. 1, 143–151 (1954).

    Article  Google Scholar 

  7. Ya. I. Frenkel’, An Introduction to the Theory of Metals [in Russian], Nauka, Leningrad (1972).

    Google Scholar 

  8. A. V. Stepanov, “On the dislocation theories of strength and plasticity of solids,” Zh. Tekh. Fiz.,23, No. 7, 1212–1218 (1953).

    CAS  Google Scholar 

  9. M. V. Bilous and M. P. Braun, Physics of Metals [in Russian], Vyshcha Shkola, Kiev (1986).

    Google Scholar 

  10. V. E. Panin, Structural Levels of Plastic Deformation and Fracture [in Russian], Nauka, Novosibirsk (1990).

    Google Scholar 

  11. V. I. Zasimchuk, E. É. Zasimchuk, and Yu. G. Gordienko, “Possible mechanism of formation of the nuclei of the channels of hydrodynamic plastic flow in crystals,” Metalofiz. Noveish. Tekhnol.,36, No. 4, 445–459 (2014).

    Article  CAS  Google Scholar 

  12. E. A. Ivanova, “Mechanical properties of the crystal lattices and nanocrystals.” Access mode: http://www.ipme.ru/ipme/labs/dms/prive/ivanova/Home_page_Elena_Ivanova/Crystal%20lattices%20RUS.htm.

  13. P. O. Esbjorn and E. J. Jensen, “Computer studies of dislocation properties using two-dimensional model systems,” J. Phys. Chem. Solids,37, No. 4, 1081–1091 (1976).

    Article  CAS  Google Scholar 

  14. M. Born, “On the stability of crystal lattices,” Proc. Cambr. Phil. Soc.,36, No. 2, 160–172 (1940); doi: https://doi.org/https://doi.org/10.1017/S0305004100017138.

  15. I. I. Novikov, Defects of the Crystal Structure of Metals [in Russian], Metallurgiya, Moscow (1975).

    Google Scholar 

  16. L. Yu. Kozak, Plasticity of Metals and Instability of Crystal Lattice [in Ukrainian], Fakel, Ivano-Frankivs’k (2004).

    Google Scholar 

  17. Z. Bojarski and Z. Wokulski, “Badania wiskerow zelaza w statycznej probie rozciagania,” Arch. Hutn.,3, No. 1, 3–26 (1980).

    Google Scholar 

  18. M. I. Gol’dshteini, V. S. Litvinov, and V. N. Bronfin, Metal Physics of High-Strength Alloys [in Russian], Metallurgiya, Moscow (1986).

    Google Scholar 

  19. S. Z. Bokshtein, S. T. Kishkin, M. P. Nazarova, and I. L. Svetlov, “Specific features of hardening of the metallic and nonmetallic filamentary single crystals,” in: Physics of Cold Hardening of Single Crystals [in Russian], Naukova Dumka, Kiev (1972), pp. 201–212.

  20. G. V. Berezhkova, Filamentary Crystals [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  21. A. M. Belikov, Plastic Deformation of Filamentary Crystals [in Russian], Izd. Voronezh Gos. Univ., Voronezh (1991).

    Google Scholar 

  22. V. I. Likhtman, P. A. Rehbinder, and G. V. Karpenko, Influence of Surface-Active Media on the Processes of Deformation of Metals [in Russian], Izd. Akad. Nauk SSSR, Moscow (1954).

    Google Scholar 

  23. L. I. Mirkin, Physical Foundations of Strength and Plasticity [in Russian], Mosk. Gos. Univ., Moscow (1968).

    Google Scholar 

  24. E. Schmidt and W. Boas, Plasticity of Crystals and, Especially, of Metallic Crystals [Russian translation], Inostr. Lit., Moscow (1938).

    Google Scholar 

  25. U. G. Bragg and U. L. Bragg, Crystalline State [Russian translation], NTI SSSR, Moscow (1938).

    Google Scholar 

  26. H. J. Gough, D. Hanson, and S. J. Wright, “The behaviour of single crystals of aluminium under static and repeated stresses,” Philos. Transact. Royal Soc.,226, 1–30 (1927).

    Google Scholar 

  27. F. R. N. Nabarro, Z. S. Bazinskii, and D. B. Kholt, Plasticity of Pure Monocrystals [in Russian], Metallurgiya, Moscow (1967).

    Google Scholar 

  28. G. P. Cherepanov, “On the general theory of fracture,” Fiz.-Khim. Mekh. Mater.,22, No. 1, 36–44 (1986).

    Google Scholar 

  29. V. P. Alekhin, Physics of the Strength and Plasticity of the Surface Layers of Materials [in Russian], Nauka, Moscow (1983).

    Google Scholar 

  30. M. A. Vasil’ev, Structure and Dynamics of the Surface of Transition Metals [in Russian], Naukova Dumka, Kiev (1988).

    Google Scholar 

  31. A. V. Bobylev, Mechanical and Technological Properties of Metals [in Russian], Metallurgiya, Moscow (1980).

    Google Scholar 

  32. V. I. Startsev, I. Ya. Il’ichev, and V. I. Pustovalov, Strength and Plasticity of Metals and Alloys at Low Temperatures [in Russian], Metallurgiya, Moscow (1975).

    Google Scholar 

  33. D. A. Wigley, Mechanical Properties of Materials at Low Temperatures, Plenum, New York (1971).

    Book  Google Scholar 

  34. E. Yu. Tonkov, Phase Diagrams of Elements under High Pressures [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  35. H. V. Karpenko, Physicochemical Mechanics of Metals [in Ukrainian], Naukova Dumka, Kyiv (1973).

    Google Scholar 

  36. G. A. Malygin, “Influence of hydrostatic pressure on the annihilation of screw dislocations by transverse sliding in alkali-haloid crystals,” Fiz. Tverd. Tela,34, No. 10, 3002–3010 (1992).

    Google Scholar 

  37. G. V. Samsonov, I. F. Pryadko, and L. F. Pryadko, Configuration Model of Substance [in Russian], Naukova Dumka, Kiev (1975).

    Google Scholar 

  38. B. I. Arkharov, Yu. G. Skripka, and E. S. Markhasin, “On the role played by the mechanism of formation of interatomic bonds in alloys in the formation of their strength and plastic properties,” Fiz.-Khim. Mekh. Mater.,14, No. 2, 47–50 (1978).

    Google Scholar 

  39. Ya. I. Dutchak, D. M. Freik, V. M. Chobanyuk, and M. O. Halushchak, Physics of Metals [in Ukrainian], NMK VO, Kyiv (1993).

    Google Scholar 

  40. W. B. Pearson, Crystal Chemistry and Physics of Metals and Alloys, Wiley, New York (1971).

    Google Scholar 

  41. R. W. Cahn, Physical Metallurgy [Russian translation], Mir, Moscow (1977).

    Google Scholar 

  42. C. Kittel, Introduction to Solid State Physics, Wiley, New York (1973).

    Google Scholar 

  43. R. Honeycomb, Plastic Deformation of Metals [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  44. A. S. Тikhonov, Effect of Superplasticity of Metals and Alloys [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  45. O. A. Kaibyshev, Superplasticity of Industrial Alloys [in Russian], Metallurgiya, Moscow (1984).

    Google Scholar 

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Correspondence to L. Yu. Kozak.

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Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 55, No. 4, pp. 7–14, July–August, 2019.

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Kozak, L.Y. New Discrete Model of Plastic Deformation of Solid Bodies. Mater Sci 55, 461–468 (2020). https://doi.org/10.1007/s11003-020-00326-z

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