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Relaxation model of dynamic plastic deformation of materials


A version of the metal plasticity relaxation model based on a plasticity integral criterion with the characteristic relaxation time parameter is suggested. The dislocation concepts of metal plasticity together with the Maxwell model for a strongly viscous fluid are used to show that this characteristic relaxation time parameter can be interpreted in terms of dissipation and energy accumulation in the case of mobile dislocations. The coincidence of the values of characteristic plastic relaxation time obtained for various descriptions of the whisker deformation allows one to conclude that the characteristic relaxation time is a basic characteristic of the material dynamic properties.

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

    Google Scholar 

  2. B. V. Petukhov, “A Theory of Sharp Yield Point in Low-Dislocation Crystals,” Zh. Tekhn. Fiz. 71(11), 42–47 (2001) [Tech. Phys. (Engl. Transl.) 46 (11), 1389–1395 (2001)].

    Google Scholar 

  3. M. A. Meyers and K. K. Chawla, Mechanical Behavior of Materials (Cambridge Univ. Press, New York, 2009).

    MATH  Google Scholar 

  4. J. R. Greer and J. Th. M. de Hosson, “Plasticity in Small-Sized Metallic Systems: Intrinsic versus Extrinsic Size Effect,” Prog. Mat. Sci. 56(6), 654–724 (2001).

    Article  Google Scholar 

  5. A. A. Gruzdkov, E. V. Sitnikova, N. F. Morozov, and Yu. V. Petrov, “Thermal Effect in Dynamic Yielding and Fracture of Metals and Alloys,” Math. Mech. Solid 14(1–2), 72–87 (2009).

    Article  MATH  MathSciNet  Google Scholar 

  6. A. A. Gruzdkov, Yu. V. Petrov, and V. I. Smirnov, “An Invariant Form of the Dynamic Criterion for Yield of Metals,” Fiz. Tverd. Tela 44(11), 1987–1989 (2002) [Phys. Solid State (Engl. Transl.) 44 (11), 2080–2082 (2002)].

    Google Scholar 

  7. A. A. Gruzdkov and Yu. V. Petrov, “On Temperature-Time Correspondence in High-Rate Deformation of Metals,” Dokl. Physics 44, 114–116 (1999).

    ADS  Google Scholar 

  8. M. M. Hutchinson, “High Upper Yield Point in Mild Steel,” J. Iron Steel Inst. 186, 431–432 (1957).

    Google Scholar 

  9. S. S. Brenner, “Plastic Deformation of Copper and Silver Whiskers,” J. Appl. Phys. 28(9), 1023–1026 (1957).

    Article  ADS  Google Scholar 

  10. R. V. Coleman, P. B. Price, and N. Cabera, “Slip of Zinc and Cadmium Whiskers,” J. Appl. Phys. 28, 1360–1361 (1957).

    ADS  Google Scholar 

  11. E. Cadoni, F. D’Aiuto, and C. Albertini, “Dynamic Behavior of Advanced High Strength Steel Used in the Automobile Structures,” DYMAT 1, 135–141 (2009).

    Google Scholar 

  12. E. N. Borodin and A. E. Mayer, “A Simple Mechanical Model for Grain Boundary Sliding in Nanocrystalline Metals,” Mat. Sci. Engng A 532, 245–248 (2012).

    Article  Google Scholar 

  13. I.N. Borodin, A. E. Mayer, Yu.V. Petrov, and A.A. Gruzdkov, “Relaxation Mechanism of Plastic Deformation and Its Justification by an Example of Sharp Yield Point,” Fiz. Tverd. Tela 57, (2014) [Phys. Solid State (Engl. Transl.)].

  14. V. S. Krasnikov, A. E. Mayer and A. P. Yalovets, “Dislocation Based High-Rate Plasticity Model and Its Application to Plate-Impact and Ultra Short Electron Irradiation Simulations,” Int. J. Plasticity 27(8), 1294–1308 (2011).

    Article  MATH  Google Scholar 

  15. A. E. Mayer, K. V. Khishchenko, P. R. Levashov, and P. N. Mayer, “Modeling of Plasticity and Fracture of Metals at Shock Loading,” J. Appl. Phys. 113, 193508 (2013).

    Article  ADS  Google Scholar 

  16. A. E. Dudorov and A. E. Mayer, “Equations of Dislocation Dynamics and Kinetics is High-Rate Plastic Deformation,” Vestnik Chelyabinsk Gos. Univ. 39(254), No. 12, 48–56 (2011).

    Google Scholar 

  17. I. S. Grigoriev and E.Z. Melikhov (Eds.), Physical Quantities. Reference Book (Energiya, Moscow, 1991) [in Russian].

    Google Scholar 

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Correspondence to I. N. Borodin.

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Original Russian Text © I.N. Borodin, Yu.V. Petrov, 2014, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2014, No. 6, pp. 41–49.

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Borodin, I.N., Petrov, Y.V. Relaxation model of dynamic plastic deformation of materials. Mech. Solids 49, 635–642 (2014).

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