Elastoplastic Strain Invariant of Metals

L. B. Zuev, S. A. Barannikova, A. G. Lunev

Institute of Strength Physics and Materials Science SB RAS, 2/4 Akademicheskiy Ave., Tomsk, 634055, Russia

Received: 21.05.2018; final version - 14.10.2018. Download: PDF logoPDF

The principal characteristic of localized plastic-flow development, known as the elastoplastic invariant of deformation, is investigated for nineteen various metals. As shown, the distribution of the experimentally obtained values of the invariant can be described by the normal distribution low. The origin of the invariant and the consequences, which describe the most important features of localized plastic flow, are discussed. As established, the principal characteristics of autowave processes of localized plasticity development, for instance, the rate and dispersion, can be calculated. It is possible to calculate the relations between the scales of localized plasticity development as well as the dependence of autowave length on the structure characteristics of metals. The relationship between the measurable invariant value and the position of metal in the (Mendeleev) Periodic table is established.

Keywords: metal, deformation, plasticity, structure, localization, strengthening, autowaves, dislocations.

PACS: 05.45.Df, 05.70.Ln, 46.35.+z, 62.20.F-, 62.20.fq, 62.30.+d, 81.40.Lm, 83.50.-v, 83.60.-a

DOI: https://doi.org/10.15407/ufm.19.04.379

Citation: L. B. Zuev, S. A. Barannikova, and A. G. Lunev, Elastoplastic Strain Invariant of Metals, Usp. Fiz. Met., 19, No. 4: 379—417 (2018) (in Russian), doi: 10.15407/ufm.19.04.379


References (88)  
  1. L. B. Zuev, V. I. Danilov, and S. A. Barannikova, Fizika Makrolokaliizatsii Plasticheskogo Techeniya [Plastic Flow Macrolocalization Physics] (Novosibirsk: Nauka: 2008) (in Russian).
  2. L. B. Zuev, V. I. Danilov, and B. S. Semukhin, Usp. Fiz. Met., 3, No. 3: 237 (2002) (in Russian). Crossref
  3. V. І. Danilov and L. B. Zuev, Usp. Fiz. Met., 9, No. 4: 371 (2008) (in Russian). Crossref
  4. L. B. Zuev, Usp. Fiz. Met., 16, No. 1: 35 (2015) (in Russian). Crossref
  5. Yu. V. Milman and I. V. Goncharova, Usp. Fiz. Met., 18, No. 3: 265 (2017) (in Russian). Crossref
  6. Yu. V. Milman, S. I. Chugunova, I. V. Goncharova, and А. А. Golubenko, Usp. Fiz. Met., 19, No. 3: 271 (2018). Crossref
  7. A. I. Olemskoi and A. A. Katsnel’son, Sinergetika Kondensirovannoi Sredy [Condensed Media Sinergetics] (Moscow: URSS: 2003) (in Russian).
  8. A. Seeger and W. Frank, Solid State Phenomena, 3–4: 125 (1988). Crossref
  9. V. A. Davydov, V. S. Zykov, and A. S. Mikhailov, Sov. Phys. Usp., 34, No. 8: 665 (1991). Crossref
  10. V. A. Davydov, N. V. Davydov, V. G. Morozov, M. N. Stolyarov, and T. Yamaguchi, Cond. Mat. Phys., 7, No. 3: 565 (2004). Crossref
  11. L. B. Zuev, V. I. Danilov, S. A. Barannikova, and V. V. Gorbatenko, Phys. Wave Phenom., 17, No. 1: 66 (2009). Crossref
  12. L. B. Zuev, Phys. Wave Phenom., 20, No. 3: 166 (2012). Crossref
  13. L. B. Zuev, V. V. Gorbatenko, and K. V. Pavlichev, Meas. Sci. Technol., 21, No. 5: 054014: 1 (2010). Crossref
  14. A. Acharia, A. Beaudoin, and R. Miller, Mathemat. Mechan. Solids, 13, Nos. 3–4: 292 (2008). Crossref
  15. C. Fressengeas, A. Beaudoin, and D. Entemeyer, Phys. Rev. B, 79, No. 1: 014108 (2009). Crossref
  16. M. A. Lebyodkin, N. P. Kobelev, and Y. Bougherira, Acta Mater., 60, No. 9: 3729 (2012). Crossref
  17. T. V. Tret’yakova and V. E. Vil’deman, Prostranstvenno-Vremennaya Neodnorodnost’ Protsessov Neuprugogo Deformirivaniya Metallov [Space-Temporary Nonhomogeneity of Anelastic Deformation in Metals] (Moscow: Fizmatlit, 2017) (in Russian).
  18. O. A. Plekhov, N. Saintier, and O. B. Naimark, Technical Physics, 52, No. 9: 1236 (2007). Crossref
  19. O. A. Plekhov, Technical Physics, 56, No. 2: 301 (2011). Crossref
  20. U. Messerschmidt, Dislocation Dynamics during Plastic Deformation (Berlin: Springer: 2010). Crossref
  21. J. Pelleg, Mechanical Properties of Materials (Dordrecht: Springer: 2013). Crossref
  22. V. A. Tatarenko, S. M. Bokoch, V. M. Nadutov, T. M. Radchenko, and Y. B. Park, Defect Diffus. Forum, 280–281: 29 (2008). Crossref
  23. T. M. Radchenko and V. A. Tatarenko, Defect Diffus. Forum, 273: 525 (2008). Crossref
  24. T. M. Radchenko, V. A. Tatarenko, H. Zapolsky, and D. Blavette, J. Alloys Compd., 452, No. 1: 122 (2008). Crossref
  25. T. M. Radchenko, V. A. Tatarenko, and H. Zapolsky, Solid State Phenom., 138: 283 (2008). Crossref
  26. R. E. Newnham, Properties of Materials (Oxford: University Press: 2005).
  27. D. Caillard and J. L. Martin, Thermally Activated Mechanisms in Crystal Plasticity (Amsterdam: Elsevier Science: 2003).
  28. M. N. Stepnov, Veroyatnostnye Metody Otsenki Kharakteristik Mekhanicheskikh Svoistv Materialov [Probability Methods of Mechanical Properties Evaluations] (Novosibirsk: Nauka Publ.: 2005) (in Russian).
  29. L. B. Zuev, Annalen der Physik, 10, Nos. 11–12: 965 (2001). Crossref
  30. L. B. Zuev, Annalen der Physik, 16, No. 4: 286 (2007). Crossref
  31. V. K. Grigorovich, Periodicheskiy Zakon Mendeleeva i Ehlektronnoe Stroenie Metallov [Mendeleev Periodic Law and Electronic Structure of Metals] (Moscow: Nauka: 1966) (in Russian).
  32. E. V. Shpolsky, Atomnaya Fizika. T. 1. Vvedenie v Atomnuyu Fiziku [Atomic physics. Vol. 1. Introduction to Atomic Physics] (Moscow: Lan: 2010) (in Russian).
  33. L. B. Zuev, Int. J. Solids Struct., 42, Nos. 3–4: 943 (2005). Crossref
  34. M. I. Kaganov, Ya. V. Kravchenko, and V. D. Natsik, Sov. Phys. Usp., 16, 878 (1974). Crossref
  35. L. I. Mirkin, Handbook of X-Ray Structural Analysis of Polycrystals (New York: Consultants Bureau: 1964).
  36. A. M. Kosevich and A. S. Kovalev, Vvedenie v Nelineinuyu Fizicheskuyu Mekhaniku [Introduction to Nonlinear Physical Mechanics] (Kyiv: Naukova Dumka: 1989) (in Russian).
  37. A. Scott, Nonlinear Science. Emergence and Dynamics of Coherent Structures (Oxford: University Press: 2003).
  38. Y. L. Klimontovich, Vvedenie v Fiziku Otkrytykh Sistem [The Introduction to Open System Physics] (Moscow: Yanus-K: 2002) (in Russian).
  39. L. B. Zuev, Tech. Phys. Lett., 31, No. 2 89 (2005). Crossref
  40. Y. B. Rumer and M. Sh. Ryvkin, Termodinamika, Statisticheskaya Fizika i Kinetica [Thermodinamics, Statistical Physics and Kinetics] (Moscow: Nauka: 1977) (in Russian).
  41. A. I. Slutsker, Phys. Solid State, 47, No. 5: 801 (2005). Crossref
  42. F. R. N. Nabarro, Strength of Metals and Alloys (Oxford: Pergamon Press: 1986).
  43. S. L. Sobolev, Sov. Phys. Usp., 34, No. 3: 217 (1991).
  44. L. S. Polak and A. S. Mikhailov, Samoorganizatsita v Neravnovesnykh Fiziko-Khimicheskikh Sistemakh [Self-Organization in Non-Equilibrium Physical-Chemical Systems] (Moscow: Nauka Publ.: 1983) (in Russian).
  45. G. R. Ivanitskii, Phys. Usp., 60, No. 7: 705 (2017). Crossref
  46. B. B. Kadomtsev, Dinamika i Informatsiya [Dynamics and Information] (Moscow: Redaktsiya UFN: 1997) (in Russian).
  47. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys., 65, No. 3: 851 (1993). Crossref
  48. L. B. Zuev, Metallofiz. Noveishie Tekhnol., 16, No. 10: 31 (1994) (in Russian).
  49. L. B. Zuev, Metallofiz. Noveishie Tekhnol., 18, No. 5: 55 (1996) (in Russian).
  50. L. B. Zuev, V. I. Danilov, and V. V. Gorbatenko, Zh. Tekhn. Fiz., 65, No. 5: 91 (1995) (in Russian).
  51. R. V. Williams, Acoustic Emission (Bristol: Adam Hilger: 1980).
  52. G. A. Malygin, Phys. Solid State, 42, No. 1: 72 (2000). Crossref
  53. D. S. Chernavsky, Sinergetika i Informatsiya. Dinamicheskaya Teoriya Informatsii [Synergetics and Information. Dynamic Information Theory] (Moscow: URSS: 2004) (in Russian).
  54. S. A. Barannikova, Tech. Phys. Lett., 30, No. 4: 338 (2004). Crossref
  55. L. B. Zuev, B. S. Semukhin, K. I. Bushmeleva, and N. V. Zarikovskaya, Phys. Met. Metallog., 89, No. 4: 423 (2000).
  56. G. Murdie, Mathematical Modelling (London: Butterworth: 1976).
  57. L. B. Zuev, N. V. Zarikovskaya, and M. A. Fedosova, Technical Physics, 55, No. 9: 1299 (2010). Crossref
  58. L. B. Zuev, N. V. Zarikovskaya, S. A. Barannikova, and G. V. Shlyakhova, Metallofiz. Noveishie Tekhnol., 35, No. 1: 113 (2013) (in Russian).
  59. J. Friedel, Dislocations (Oxford: Pergamon, 1964).
  60. J. P. Hirth and J. Lothe, Theory of Dislocations (New York: McGraw-Hill Book Comp.: 1970)
  61. M. Zaiser and A. Seeger, Dislocations in Solids (Amsterdam: Elsevier: 2002).
  62. L. B. Zuev and V. I. Danilov, Phil. Mag. A, 79, No. 1: 43 (1999). Crossref
  63. L. D. Landau and E. M. Lifshits, Gidrodinamika [Fluid Mechanics] (Moscow: Nauka: 1988) (in Russian).
  64. M. Zaiser and E. C. Aifantis, Int. J. Plasticity, 22, No. 8: 1432 (2006). Crossref
  65. G. A. Malygin, Phys. Usp., 54, No. 11: 1091 (2011). Crossref
  66. A. N. Kolmogorov, I. G. Petrovskii, and N. S. Piskunov, Bull. MGU. Ser. А. Matemat. i Mekhan., 1, No. 1: 6 (1937).
  67. E. F. Mitshenko, V. A. Sadovnithii, A. Y. Kolesov, and N. Kh. Rozov, Avtovolnovye Protsessy v Nelineinykh Sredakh s Diffuziei [Autowave Processes in Nonlinear Media with Diffusion] (Moscow: Fizmatlit: 2010) (in Russian).
  68. V. A. Vasil’ev, Y. M. Romanovckii, and V. G. Yakhno, Avtovolnovye Protsessy [Autowave Processes] (Moscow: Nauka: 1987) (in Russian).
  69. J. J. Gilman, J. Appl. Phys., 36, No. 9: 2772 (1965). Crossref
  70. L. B. Zuev, Izvestia RAN. Ser. Fizicheskaya, 78, No. 10: 957 (2014) (in Russian).
  71. R. Hill, The Mathematical Theory of Plasticity (Oxford: University Press, 1998).
  72. A. V. Porubov, Lokalizatsiya Nelineinykh Voln Deformatsii [The Localization of Non-Linear Waves of Deformation] (Moscow: Fizmatlit, 2009) (in Russian).
  73. L. B. Zuev and B. S. Semukhin, Phil. Mag. A, 82, No. 6: 1183 (2002). Crossref
  74. K. Otsuka and K. Shimizu, Int. Met. Rev., 31, No. 3: 93 (1986). Crossref
  75. E. M. Nadgorny, Nesovershenstva Kristallicheskogo Stroeniya i Martensitnye Prevrashcheniya [Imperfection of the Crystalline Structure and Martensitic Transformations] (Moscow: Nauka: 1972) (in Russian).
  76. T. Suzuki. H. Yoshinaga, and S. Takeuchi, Dynamics of Dislocations and Plasticity (Springer-Verlag Berlin Heidelberg: 1991). Crossref
  77. V. I. Alshits and V. L. Indenbom, Dislocations in Solids, Vol. 12 (Ed. F. R. N. Nabarro and J. P. Hirth) (Amsterdam: Elsevier: 2004).
  78. S. A. Barannikova, M. V. Nadezhkin, and L. B. Zuev, Phys. Solid State, 52, No. 7: 1382 (2010). Crossref
  79. S. A. Barannikova, M. V. Nadezhkin, and L. B. Zuev, Tech. Phys. Let, 37: 750 (2011). Crossref
  80. L. B. Zuev, S. A. Barannikova, M. V. Nadezhkin, and V. V. Gorbatenko, J. Min. Sci., 50, No. 1: 43 (2014). Crossref
  81. L. B. Zuev, S. A. Barannikova, and V. I. Danilov, Crystallogr. Rep., 54, No. 6: 1011 (2009). Crossref
  82. L. B. Zuev and S. A. Barannikova, Metallofiz. Noveishie Tekhnol., 31, No. 5: 711 (2009) (in Russian).
  83. L. B. Zuev and S. A. Barannikova, Int. J. Mech. Sci., 88, No. 12: 1 (2014). Crossref
  84. P. Hähner, Appl. Phys. A, 58, No. 4: 41 (1994). Crossref
  85. E. C. Aifantis, Acta Mech., 225, Nos. 4–5: 999 (2014). Crossref
  86. D. Caillard, Acta Mater., 58, No. 9: 3493 (2010). Crossref
  87. E. V. Kozlov, V. A. Starenchenko, and N. A. Koneva, Metally, No. 5: 152 (1993) (in Russian).
  88. B. A. Movchan, S. A. Firstov, and Yu. F. Lugovskoy, Struktura, Prochnost’ i Soprotivlenie Ustalosti Mikrokristallicheskikh i Mikrosloinykh Materialov [Structure, Strength and Resistance of Fatigue of Microcrystalline and Microlayer Materials] (Kiev: Naukova Dumka: 2015) (in Russian).