Skip to main content
SpringerLink
Log in

Instabilities of Dynamic Strain Diagrams Predicted by the Relaxation Model of Plasticity

  • Research Paper
  • Published:
Journal of Dynamic Behavior of Materials Aims and scope Submit manuscript

Abstract

To predict of appearance and disappearance of yield drop effects with regard to different dynamics, temperatures or other factors, the wide spectrum of the initial plastic stage of stress–strain diagrams for homogeneous materials is considered. Compared with unchanged quasi-static stress–strain diagrams, the dynamic changes in stress–strain diagrams depending on loading history are classified. In addition to a group of monotonic diagrams, varying only in yield strength, a group of three nonmonotonic diagrams, with the appearance or disappearance of the yield drop effect at different strain rates, is predicted on the basis of the relaxation model of plasticity. It is shown that unlike classical dynamic plasticity models, which are able to construct only the first set of diagrams, the relaxation model of plasticity allows the prediction of any set of deformation curves on the basis of a minimal number of parameters, which are invariant to the strain rate and generally to the loading history. Based on experimental data from the literature, dynamic deformation dependencies with an emerging yield drop at a fixed strain rate for different metals are predicted. Similar dynamic effects on stress–strain diagrams for materials with different strain rate sensitivities and structural-temporal parameters are revealed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Selyutina NS, Petrov YuV (2018) Comparative analysis of dynamic plasticity models. Rev Adv Mater Sci 57:199–211. https://doi.org/10.1515/rams-2018-0065

    Article  CAS  Google Scholar 

  2. Johnson GR, Cook WH (1985) Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng Fract Mech 21(1):31–48. https://doi.org/10.1016/0013-7944(85)90052-9

    Article  Google Scholar 

  3. Zerilli FG, Armstrong RW (1987) Dislocation-mechanics-based constitutive relations for material dynamics calculations. J Appl Phys 61(5):1816–1825. https://doi.org/10.1063/1.338024

    Article  CAS  Google Scholar 

  4. Couque H, Boulanger R, Bornet F (2006) A modified Johnson-Cook model for strain rates ranging from 10–3 to 105 s–1. J Phys IV: J 134:87–93. https://doi.org/10.1051/jp4:2006134015

    Article  CAS  Google Scholar 

  5. Kang WJ, Cho SS, Huh H, Chung DT (1999) Modified Johnson-Cook model for vehicle body crashworthiness simulation. Int J Vehicle Des 21(4–5):424–435

    Article  Google Scholar 

  6. Khan AS, Suh YS, Kazmi R (2004) Quasi-static and dynamic loading responses and constitutive modeling of titanium alloys. Int J Plast 20(12):2233–2248. https://doi.org/10.1016/j.ijplas.2003.06.005

    Article  CAS  Google Scholar 

  7. Rusinek A, Klepaczko JR (2001) Shear of a sheet steel at wide range of strain rates and a constitutive relation with strain-rate and temperature dependence of the flow stress. Int J Plast 17(1):87–115. https://doi.org/10.1016/S0749-6419(00)00020-6

    Article  CAS  Google Scholar 

  8. Johnston WG (1962) Yield points and delay times in single crystals. J Appl Phys 33:2716–2730. https://doi.org/10.1063/1.1702538

    Article  CAS  Google Scholar 

  9. Brenner SS (1957) Plastic deformation of copper and silver whiskers. J Appl Phys 28(9):1023–1026. https://doi.org/10.1063/1.1722900

    Article  CAS  Google Scholar 

  10. Rajaraman S, Jonnalagadda KN, Ghosh P (2013) Indentation and dynamic compression experiments on microcrystalline and nanocrystalline nickel. C Proc Soc Exp Mech 1:157–163. https://doi.org/10.1007/978-1-4614-4238-7_20

    Article  Google Scholar 

  11. Laber K, Kawałek A, Sawicki S, Dyja H, Borowski J, Lesniak D, Jurczak H (2016) Investigations of plasticity of hard-deformed aluminium alloys of 5xxx series using torsion plastometer. Arch Metall Mater 61(4):1853–1860

    Article  CAS  Google Scholar 

  12. Petrov YV, Borodin EN (2015) Relaxation mechanism of plastic deformation and its justification using the example of the sharp yield point phenomenon in whiskers. Phys Solid State 57(2):353–359. https://doi.org/10.1134/S1063783415020286

    Article  CAS  Google Scholar 

  13. Selyutina N, Borodin EN, Petrov Y, Mayer AE (2016) The definition of characteristic times of plastic relaxation by dislocation slip and grain boundary sliding in copper and nickel. Int J Plast 82:97–111. https://doi.org/10.1016/j.ijplas.2016.02.004

    Article  CAS  Google Scholar 

  14. Selyutina NS, Petrov YuV (2018) Prediction of the dynamic yield strength of metals using two structural-temporal parameters. Phys Solid State 60(2):244–249. https://doi.org/10.1134/S1063783418020221

    Article  CAS  Google Scholar 

  15. Petrov YV, Gruzdkov AA, Bratov VA (2012) Structural-temporal theory of fracture as a multiscale process. Phys Mesomech 15(3–4):232–237. https://doi.org/10.1134/S1029959912020117

    Article  Google Scholar 

  16. Petrov YuV, Smirnov IV, Volkov GA, Abramian AK, Bragov AM, Verichev SN (2017) Dynamic failure of dry and fully saturated limestone samples based on incubation time concept. J Rock Mech Geotech Eng 9(1):125–134. https://doi.org/10.1016/j.jrmge.2016.09.004

    Article  Google Scholar 

  17. Evstifeev A, Kazarinov N, Petrov Y, Witek L, Bednarz A (2018) Experimental and theoretical analysis of solid particle erosion of a steel compressor blade based on incubation time concept. Eng Fail Anal 87:15–21. https://doi.org/10.1016/j.engfailanal.2018.01.006

    Article  CAS  Google Scholar 

  18. Selyutina NS, Borodin EN, Petrov YV (2018) Structural-temporal peculiarities of dynamic deformation of nanostructured and nanoscaled metals. Phys Solid State 60(9):1813–1820. https://doi.org/10.1134/S1063783418090275

    Article  CAS  Google Scholar 

  19. Borodin EN, Mayer AE, Petrov YuV, Gruzdkov AA (2014) Maximum yield strength under quasi-static and high-rate plastic deformation of metals. Phys Solid State 56(12):2470–2479. https://doi.org/10.1134/S1063783414120051

    Article  CAS  Google Scholar 

  20. Selyutina NS, Petrov YuV (2019) Modeling the time effects of irreversible deformation based on the relaxation plasticity model. Phys Solid State 61(6):935–940. https://doi.org/10.1134/S1063783419060222

    Article  CAS  Google Scholar 

  21. Selyutina NS (2020) Temperature relaxation model of plasticity for metals under dynamic loading. Mech Mater 150:103589. https://doi.org/10.1016/j.mechmat.2020.103589

    Article  Google Scholar 

  22. Gruzdkov AA, Petrov YuV (1999) On temperature-time correspondence in high-rate deformation of metals. Dokl Phys 44(2):114–116

    Google Scholar 

  23. Petrov YuV, Gruzdkov AA, Sitnikova EV (2007) Anomalous behavior of yield stress upon an increase in temperature under high strain rate conditions. Dokl Phys 52(12):691–694. https://doi.org/10.1134/S1028335807120129

    Article  CAS  Google Scholar 

  24. Petrov Y (2014) Fracture, electric breakdown and phase transformations under impact loading. Proc Mat Sci 3:467–472. https://doi.org/10.1016/j.mspro.2014.06.078

    Article  CAS  Google Scholar 

  25. Gruzdkov AA, Petrov YuV, Smirnov VI (2002) An invariant form of the dynamic criterion for yield of metals. Phys Solid State 44(11):2080–2082. https://doi.org/10.1134/1.1521459

    Article  CAS  Google Scholar 

  26. Wei Q, Schuster BE, Mathaudhu SN, Hartwig KT, Kecskes LJ, Dowding RJ, Ramesh KT (2008) Dynamic behaviors of body-centered cubic metals with ultrafine grained and nanocrystalline microstructures. Mater Sci Eng A 493:58–64. https://doi.org/10.1016/j.msea.2007.05.126

    Article  CAS  Google Scholar 

  27. Sun X, Soulami A, Choi KS, Guzman O, Chen W (2012) Effects of sample geometry and loading rate on tensile ductility of TRIP800 steel. Mater Sci Engng A 541:1–7. https://doi.org/10.1016/j.msea.2011.12.115

    Article  CAS  Google Scholar 

  28. Cadoni E, Forni D (2015) Strain rate effects on reinforcing steels in tension. EPJ Web Conf 94:01004. https://doi.org/10.1051/epjconf/20159401004

    Article  Google Scholar 

  29. Khan AS, Zhang H, Takacs L (2000) Mechanical response and modeling of fully compacted nanocrystalline iron and copper. Int J Plast 16:1459–1476. https://doi.org/10.1016/S0749-6419(00)00023-1

    Article  CAS  Google Scholar 

  30. Uenishi A, Teodosiu C (2004) Constitutive modelling of the high strain rate behaviour of interstitial-free steel. Int J Plast 20:915–936. https://doi.org/10.1016/j.ijplas.2003.06.004

    Article  CAS  Google Scholar 

  31. Liu W, He Z, Tang C, Chen Y (2016) Effect of deformation condition on dynamic mechanical properties and microstructure evolution of 2519A Aluminum Alloy. J Mater Eng 44(1):47–53. https://doi.org/10.11868/j.issn.1001-4381.2016.01.007

    Article  CAS  Google Scholar 

  32. Zhang X, Li H, Li H, Gao H, Gao Z, Liu Y, Liu B (2008) Dynamic property evaluation of aluminum alloy 2519A by split Hopkinson pressure bar. Trans Nonferrous Metals Soc China 18:1–5. https://doi.org/10.1016/S1003-6326(08)60001-1

    Article  Google Scholar 

Download references

Acknowledgements

The study was supported by the Russian Science Foundation (Grant 21-71-00046).

Author information

Authors and Affiliations

  1. Saint Petersburg State University, 199034, Universitetskaya nab. 7/9, St. Petersburg, Russia

    N. S. Selyutina & Y. V. Petrov

  2. Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., 199178 Bolshoj pr., 61, St. Petersburg, Russia

    N. S. Selyutina & Y. V. Petrov

Authors
  1. N. S. Selyutina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. V. Petrov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. S. Selyutina.

Ethics declarations

Conflict of interest

The authors declared that they have no conflicts of interest in this work.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Selyutina, N.S., Petrov, Y.V. Instabilities of Dynamic Strain Diagrams Predicted by the Relaxation Model of Plasticity. J. dynamic behavior mater. 8, 304–315 (2022). https://doi.org/10.1007/s40870-022-00334-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40870-022-00334-x

Keywords

Search

Navigation