Russian Metallurgy (Metally)

, Volume 2018, Issue 9, pp 867–879 | Cite as

Effect of Recovery and Recrystallization on the Hall–Petch Relation Parameters in Submicrocrystalline Metals: III. Model for the Effect of Recovery and Recrystallization on the Hall–Petch Relation Parameters

  • V. N. Chuvil’deev
  • A. V. NokhrinEmail author
  • M. M. Myshlyaev
  • V. I. Kopylov
  • Yu. G. Lopatin
  • N. V. Melekhin
  • A. V. Piskunov
  • A. A. Bobrov
  • O. E. Pirozhnikova


A theoretical model is developed to describe the influence of recovery and recrystallization on the macroelastic limit, the yield strength, and the grain-boundary hardening coefficient of the submicrocrystalline (SMC) metals fabricated by severe plastic deformation. The anomalous hardening and the increase in the grain-boundary hardening coefficient upon annealing of the SMC metals are shown to be related to defect accumulation in migrating grain boundaries in them. Equations are derived to relate the Hall–Petch relation parameters to the grain-boundary migration velocity, the nonequilibrium state of grain boundaries, the lattice dislocation density, and the annealing temperature and time. The results of the numerical calculations performed using the developed model are compared with the experimental results obtained in part I of this work.


submicrocrystalline metals Hall–Petch relation grain boundaries diffusion anomalous hardening recovery recrystallization 



This work was supported by the Russian Foundation for Basic Research (project no. 15-08-09298) and the Ministry of Education and Science of the Russian Federation (project no. 11.5944.2017/6.7 in terms of a state task for institutes of higher education).


  1. 1.
    V. M. Segal, I. J. Beyerlein, C. N. Tome, V. N. Chuvil’deev, and V. I. Kopylov, Fundamentals and Engineering of Severe Plastic Deformation (Nova Sci. Publ., New York, 2010).Google Scholar
  2. 2.
    V. N. Chuvil’deev, Nonequilibrium Grain Boundaries in Metals. Theory and Applications (Fizmatlit, Moscow, 2004).Google Scholar
  3. 3.
    V. N. Chuvil’deev, V. I. Kopylov, and W. Zeiger, “Non-equilibrium grain boundaries. Theory and its applications for describing nano- and microcrystalline materials processed by ECAP,” Ann. Chimie: Sci. Mater. 27 (3), 55–64 (2002).CrossRefGoogle Scholar
  4. 4.
    V. A. Likhachev and R. Yu. Khairov, Introduction to the Theory of Disclinations (Izd. LGU, Leningrad, 1975).Google Scholar
  5. 5.
    V. N. Chuvil’deev, “Micromechanism of deformation-stimulated grain-boundary self-diffusion: II. Effect of lattice dislocations introduced into grain boundaries on the diffusion properties of grain boundaries,” Phys. Met. Metallogr. 81 (6), 583–588 (1996).Google Scholar
  6. 6.
    V. N. Chuvil’deev and O. E. Pirozhnikova, “Micromechanism of deformation-stimulated grain-boundary self-diffusion: III. Effect of lattice dislocation fluxes on the diffusion properties of grain boundaries,” Phys. Met. Metallogr. 82 (1), 71–77 (1996).Google Scholar
  7. 7.
    N. I. Noskova and R. R. Mulyukov, Submicrocrystalline and Nanocrystalline Metals and Alloys (UrO RAN, Yekaterinburg, 2003).Google Scholar
  8. 8.
    E. V. Kozlov, A. M. Glezer, N. A. Koneva, N. A. Popova, and I. A. Kurzina, Fundamentals of the Plastic Deformation of Nanostructured Materials, Ed. by A. M. Glezer (Fizmatlit, Moscow, 2016).Google Scholar
  9. 9.
    V. N. Chuvil’deev, O. E. Pirozhnikova, A. V. Nokhrin, and M. M. Myshlyaev, “Strain hardening under structural superplasticity,” Fiz. Tverd. Tela 49 (4), 650–657 (2007).Google Scholar
  10. 10.
    V. N. Chuvil’deev, A. V. Nokhrin, V. I. Kopylov, M. Yu. Gryaznov, O. E. Pirozhnikova, and Yu. G. Lopatin, “Effect of a simultaneous increase in strength and plasticity at room temperature in the nano- and microcrystalline metals fabricated by severe plastic deformation. Part I. Model for calculating the limiting strength and plasticity at room temperature,” Materialoved., No. 12, 2–10 (2010).Google Scholar
  11. 11.
    V. N. Chuvil’deev, “Free volume of grain boundaries and the deformation behavior of materials under structural superplasticity,” Materialoved., No. 3, 20–25 (1999).Google Scholar
  12. 12.
    V. A. Pozdnyakov, “Mechanisms of plastic deformation and the anomalies of the Hall–Petch dependence in metallic nanocrystalline materials,” Phys. Met. Metallogr. 96 (1), 105–119 (2001).Google Scholar
  13. 13.
    V. N. Perevezentsev, V. V. Rybin, and V. N. Chuvil’deev, “The theory of structural superplasticity: II. Accumulation of defects on the intergranular and interphase boundaries. Accommodation of the grain-boundary sliding. The upper bound of the superplastic strain rate,” Acta Met. Mater. 40 (6), 895–905 (1992).CrossRefGoogle Scholar
  14. 14.
    V. N. Chuvil’deev, O. E. Pirozhnikova, and A. V. Petryaev, “Micromechanisms of grain-boundary recovery upon annealing after deformation: I. Recovery of diffusional properties of grain boundaries,” Phys. Met. Metallogr. 92 (6), 540–545 (2001).Google Scholar
  15. 15.
    A. V. Petryaev and V. N. Chuvil’deev, “Micromechanisms of grain-boundary recovery upon annealing after deformation: II. Recovery of yield strength in fine-grained materials,” Phys. Met. Metallogr. 92 (6), 546–552 (2001).Google Scholar
  16. 16.
    R. Z. Valiev and T. G. Langdon, “Principles of equal-channel angular pressing as a processing tool for grain refinement,” Prog. Mater. Sci. 51 (7), 881–981 (2006).CrossRefGoogle Scholar
  17. 17.
    A. P. Zhilyaev and T. G. Langdon, “Using high-pressure torsion for metal processing: fundamentals and applications,” Prog. Mater. Sci. 53 (6), 893–979 (2008).CrossRefGoogle Scholar
  18. 18.
    J. P. Hirth and J. Lothe, Theory of Dislocations (McGraw-Hill, New York, 1967).Google Scholar
  19. 19.
    M. I. Goldshtein, V. S. Litvinov, and B. M. Bronfin, Physical Metallurgy of High-Strength Alloys (Metallurgiya, Moscow, 1986).Google Scholar
  20. 20.
    X. Molodova, G. Gottstein, M. Winning, and R. J. Hellmig, “Thermal stability of ECAP processed pure copper,” Mater. Sci. Eng. A 460–461, 204–213 (2007).Google Scholar
  21. 21.
    A. V. Nokhrin, V. N. Chuvil’deev, E. S. Smirnova, I. M. Makarov, Yu. G. Lopatin, and V. I. Kopylov, “Thermal stability of the structure of single-crystalline metals produced by equal-channel angular pressing,” Russ. Metall. (Metally), No. 2, 126–140 (2004).Google Scholar
  22. 22.
    V. N. Chuvil’deev, V. I. Kopylov, A. V. Nokhrin, I. M. Makarov, L. M. Malashenko, and V. A. Kukareko, “Recrystallization in microcrystalline copper and nickel produced by equal-channel angular pressing: I. Structural investigations. Effect of anomalous growth,” Fiz. Met. Metalloved. 96 (5), 51–60 (2003).Google Scholar
  23. 23.
    S. S. Gorelik, Recrystallization of Metals and Alloys (Metallurgiya, Moscow, 1967).Google Scholar
  24. 24.
    Yu. V. Ivanisenko, A. A. Sirenko, and A. V. Korznikov, “Effect of heating on the structure and mechanical properties of submicron-grained armco iron,” Fiz. Met. Metalloved. 87 (4), 78–83 (1999).Google Scholar
  25. 25.
    A. V. Korznikov, S. Idrisova, and N. I. Noskova, “Structure and thermal stability of submicron-grained molybdenum,” Phys. Met. Metallogr. 85 (3), 327–331 (1998).Google Scholar
  26. 26.
    A. V. Korznikov, I. M. Safarov, D. V. Laptenok, B. F. Abdulin, and R. Z. Valiev, “Structure and hardness of oxidized iron compacts with an ultrafine grain,” Metals, No. 4, 131–136 (1993).Google Scholar
  27. 27.
    R. Z. Valiev, A. V. Sergueeva, and A. K. Mukherjee, “The effect of annealing on tensile deformation behavior of nanostructured SPD titanium,” Scr. Mater. 49 (7), 669–674 (2003).CrossRefGoogle Scholar
  28. 28.
    V. N. Chuvil’deev, A. V. Nokhrin, and V. I. Kopylov, “Anomalous strengthening upon annealing of microcrystalline metals produced by high-cycle equal-channel angular pressing,” Russ. Metall. (Metally), No. 3, 240–251 (2003).Google Scholar
  29. 29.
    G. G. Frost and M. F. Eshbi, Deformation-Mechanism Maps (Pergamon, Oxford, 1982).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • V. N. Chuvil’deev
    • 1
  • A. V. Nokhrin
    • 1
    Email author
  • M. M. Myshlyaev
    • 2
    • 3
  • V. I. Kopylov
    • 1
    • 4
  • Yu. G. Lopatin
    • 1
  • N. V. Melekhin
    • 1
  • A. V. Piskunov
    • 1
  • A. A. Bobrov
    • 1
  • O. E. Pirozhnikova
    • 1
  1. 1.Nizhny Novgorod State UniversityNizhny NovgorodRussia
  2. 2.Baikov Institute of Metallurgy and Materials Science, Russian Academy of SciencesMoscowRussia
  3. 3.Institute of Solid State Physics, Russian Academy of SciencesChernogolovkaRussia
  4. 4.Physicotechnical Institute, Belarussian Academy of SciencesMinskBelarus

Personalised recommendations