Skip to main content
SpringerLink
Log in

Dispersion correction in split-Hopkinson pressure bar: theoretical and experimental analysis

  • Original Article
  • Published:
Continuum Mechanics and Thermodynamics Aims and scope Submit manuscript

Abstract

The paper presents experimental and mathematical analysis of the dispersion effect of pulses, which propagate along an elastic bar whose cross section has a finite radius. In some cases, dispersion can influence significantly the interpretation of the experimental data, obtained in experimental schemes, which are based on using measuring bars for investigation material behavior at high strain rates (the split-Hopkinson pressure bar method and its modifications). Solutions for the Pochhammer–Chree equation are obtained for various measuring bars used in experimental setups in the Research Institute for Mechanics of Lobachevsky State University of Nizhny Novgorod. The procedure of pulse shift accounting for dispersion has been implemented and tested on the basis of our experimental data and the data available in the existing scientific literature. This procedure was employed to analyze the influence of pulse shape on the degree of its change in shape during its propagation along a measuring bar. It is shown how the procedure of dispersion shift improves the quality of interpretation of primary experimental data for some materials.

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

Similar content being viewed by others

References

  1. Kolsky, H.: An investigation of the mechanical properties of materials at very high rates of loading. Proc. Phys. Soc. Lond. Sect. B 62, 676–700 (1949)

    Article  ADS  Google Scholar 

  2. Engelbrecht, J., Berezovski, A.: Reflections on mathematical models of deformation waves in elastic microstructured solids. Math. Mech. Complex Syst. 3(1), 43–82 (2015)

    Article  MathSciNet  Google Scholar 

  3. Altenbach, H., Eremeyev, V.A., Lebedev, L.P., Rendón, L.A.: Acceleration waves and ellipticity in thermoelastic micropolar media. Arch. Appl. Mech. 80(3), 217–227 (2010)

    Article  ADS  Google Scholar 

  4. Rosi, G., Placidi, L., Nguyen, V.H., Naili, S.: Wave propagation across a finite heterogeneous interphase modeled as an interface with material properties. Mech. Res. Commun. 84, 43–48 (2017)

    Article  Google Scholar 

  5. dell’Isola, F., Madeo, A., Placidi, L.: Linear plane wave propagation and normal transmission and reflection at discontinuity surfaces in second gradient 3D continua. Z. Angew. Math. Mech. 92(1), 52–71 (2012)

    Article  MathSciNet  Google Scholar 

  6. Davies, R.M.: A critical study of the Hopkinson pressure bar. Philos. Trans. R. Soc. Lond. Ser. A 240(821), 375–457 (1948)

    Article  ADS  Google Scholar 

  7. Follansbee, P.S., Frantz, C.: Wave propagation in the split Hopkinson pressure bar. ASME J. Eng. Mater. Technol. 105, 61–66 (1983)

    Article  Google Scholar 

  8. Gong, J.C., Malvern, L.E., Jenkins, D.A.: Dispersion investigation in the split Hopkinson pressure bar. ASME J. Eng. Mater. Technol. 112, 309–314 (1990)

    Article  Google Scholar 

  9. Lifshitz, J.M., Leber, H.: Data processing in the split Hopkinson pressure bar tests. Int. J. Impact Eng. 15(6), 723–733 (1994)

    Article  Google Scholar 

  10. Bragov, A.M., Konstantinov, A.Y., Medvedkina, M.V.: Wave dispersion in split Hopkinson pressure bars in dynamic testing of brittle materials. Vestn. Lobachevsky Univ. Nizhni Novgorod 6(1), 158–162 (2011). ISSN: 1993-1778

    Google Scholar 

  11. Pochhammer, L.: Uber Fortplanzungsgeschwindigkeiten kleiner Schwingungen in einem unbergrenzten isotropen Kreiszylinder. J. Reine Angew. Math. 81, 324 (1876). (German)

    MathSciNet  Google Scholar 

  12. Bancroft, D.: The velocity of longitudinal wave in cylindrical bars. Phys. Rev. 59, 588–593 (1941)

    Article  ADS  Google Scholar 

  13. Le, K.C.: Vibrations of Shells and Rods. Springer, Berlin (1999)

    Book  Google Scholar 

  14. Yew, E.H., Chen, C.S.: Experimental study of dispersive waves in beam and rod using FFT. ASME J. Appl. Mech. 45, 375–457 (1978)

    Article  Google Scholar 

  15. Gorham, D.: A numerical method for the correction of dispersion in pressure bar signals. J. Phys. E Sci. Instrum. 16, 477–479 (1983)

    Article  ADS  Google Scholar 

  16. Follansbee, P., Frantz, C.: Wave propagation in the split Hopkinson pressure bar. J. Eng. Mater. Technol. 105, 61–66 (1983)

    Article  Google Scholar 

  17. Rigby, S.E., Barr, A.D., Clayton, M.: A review of Pochhammer–Chree dispersion in the Hopkinson bar. Proc. Inst. Civ. Eng. Eng. Comput. Mech. 171(1), 3–13 (2018). https://doi.org/10.1680/jencm.16.00027

    Article  Google Scholar 

  18. Lee, C., Crawford, R.: A new method for analysing dispersed bar gauge data. Meas. Sci. Technol. 4, 931–937 (1993)

    Article  ADS  Google Scholar 

  19. Lee, C., Crawford, R., Mann, K., Coleman, P., Petersen, C.: Evidence of higher Pochhammer–Chree modes in an unsplit Hopkinson bar. Meas. Sci. Technol. 6, 853–859 (1995)

    Article  ADS  Google Scholar 

  20. Puckett, A.: An experimental and theoretical investigation of axially symmetric wave propagation in thick cylindrical waveguides. PhD thesis, The Graduate School, The Unversity of Maine, USA (2004)

  21. Husemeyer, P.: Theoretical and numerical investigation of multiple-mode dispersion in Hopkinson bars. PhD thesis, Blast Impact and Survivability Research Unit, Department of Mechanical Engineering, University of Cape Town, South Africa (2011)

  22. Gama, B.A., Lopatnikov, S.L., Gillespie Jr., J.W.: Hopkinson bar experimental technique: a critical review. Appl. Mech. Rev. (2004). https://doi.org/10.1115/1.1704626

    Article  Google Scholar 

  23. Li, Z., Lambros, J.: Determination of the dynamic response of brittle composites by the use of split Hopkinson pressure bar. Compos. Sci. Technol. 59, 1097–1107 (1999)

    Article  Google Scholar 

  24. Klepaczko, J.: Advanced experimental techniques in material testing. In: Nowacki, W.K., Klepachko, J.R. (eds.) New Experimental Methods in Material Dynamics and Impact. Trends in Mechanics of Materials, pp. 1–58. Institute of Fundamental Technological Research Polish Academy of Sciences, Warsaw (2001)

  25. Bacon, C.: An experimental method for considering dispersion and attenuation in a viscoelastic Hopkinson bar. Exp. Mech. 38, 242 (1998). https://doi.org/10.1007/BF02410385

    Article  Google Scholar 

  26. Ramirez, H., Rubio-Gonzalez, C.: Finite-element simulation of wave propagation and dispersion in Hopkinson bar test. Mater. Des. 27, 36–44 (2006)

    Article  Google Scholar 

  27. Le, K.C.: High-frequency longitudinal vibrations of elastic rods. J. Appl. Math. Mech. (PMM) 50, 335–341 (1986)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The theoretical part of work was carried out by a Grant from the Russian Science Foundation (Project No. 17-79-20161). The experimental part of work was done in the frame of the state task of the Ministry of Education and Science of the Russian Federation No. 9.6109.2017/6.7.

Author information

Authors and Affiliations

  1. Research Institute for Mechanics, National Research Lobachevsky State University of Nizhny Novgorod, 23 Prospekt Gagarina (Gagarin Avenue) BLDG 6, Nizhny Novgorod, Russian Federation, 603950

    Anatolii Mikhailovich Bragov, Andrei Kirillovich Lomunov, Dmitrii Aleksandrovich Lamzin & Aleksandr Yurevich Konstantinov

Authors
  1. Anatolii Mikhailovich Bragov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrei Kirillovich Lomunov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dmitrii Aleksandrovich Lamzin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Aleksandr Yurevich Konstantinov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anatolii Mikhailovich Bragov.

Additional information

Communicated by Victor Eremeyev and Holm Altenbach.

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

Bragov, A.M., Lomunov, A.K., Lamzin, D.A. et al. Dispersion correction in split-Hopkinson pressure bar: theoretical and experimental analysis. Continuum Mech. Thermodyn. 34, 895–907 (2022). https://doi.org/10.1007/s00161-019-00776-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00161-019-00776-0

Keywords

Search

Navigation