Skip to main content
SpringerLink
Log in

An experimental method for considering dispersion and attenuation in a viscoelastic Hopkinson bar

  • Published:
Experimental Mechanics Aims and scope Submit manuscript

Abstract

An experimental method is developed to perform Hopkinson tests by means of viscoelastic bars by considering the wave propagation attenuation and dispersion due to the material rheological properties and the bar radial inertia (geometric effect). A propagation coefficient, representative of the wave dispersion and attenuation, is evaluated experimentally. Thus, the Pochhammer and Chree frequency equation is not necessary. Any bar cross-section shapes can be employed, and the knowledge of the bar mechanical properties is useless. The propagation coefficients for two PMMA bars with different diameters and for an elastic aluminum alloy bar are evaluated. These coefficients are used to determine the normal forces at the free end of a bar and at the ends of two bars held in contact. As an application, the mechanical impedance of an accelerometer is evaluated.

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

Abbreviations

a :

bar radius

A :

cross-sectional area of the bar

c(ω):

phase velocity

c 0 :

one-dimensional elastic wave speed

d :

distance between the strain gage location and the nonimpacted end

E :

Young's modulus

E *(ω):

complex Young's modulus

\(\tilde f(x,\omega )\) :

Fourier transform of functionf(x, t) at cross sectionx

F :

normal force

H *(ω):

strain transfer function

k(w):

wave number

L :

bar length

m :

accelerometer mass

\(\tilde N(\omega )\) :

Fourier transform of the strain atx=0 due to the wave traveling in the direction of decreasingx

\(\tilde P(\omega )\) :

Fourier transform of the strain atx=0 due to the wave traveling in the direction of increasingx

t :

time

u :

axial displacement

v :

axial particle velocity

Z *(ω):

mechanical impedance

α(ω):

attenuation coefficient

ε:

longitudinal strain

εI(t):

longitudinal strain due to the incident wave

ε R (t):

longitudinal strain due to the reflected wave

γ(ω):

propagation coefficient

ν:

frequency

ω:

angular frequency

ρ:

mass density of the bar

σ:

normal stress

References

  1. Kolsky, H., Stress Waves in Solids, Dover, New York (1963).

    Google Scholar 

  2. Lundberg, B. andHenchoz, A., “Analysis of Elastic Waves from Two-point Strain Measurement,” EXPERIMENTAL MECHANICS,17,213–218 (1977).

    Article  Google Scholar 

  3. Bacon, C. “Mesure de la ténacité dynamique de matériaux fragiles en flexion-trois-points à haute température—Utilisation des barres de Hopkinson,” Ph.D. thesis, Université Bordeaux, 1, No. 840 (1993).

  4. Lundberg, B., Carlsson, J., andSundin, K.G., “Analysis of Elastic Waves in Non-uniform Rods from Two-point Strain Measurement,”J. Sound Vibration,137,483–493 (1990).

    Article  Google Scholar 

  5. Bacon, C., Carlsson, J., andLataillade, J.L., “Evaluation of Force and Particle Velocity at the Heated End of a Rod Subjected to Impact Loading,”J. Physique IV, Colloque C3,1,395–401 (1991).

    Google Scholar 

  6. Bacon, C., Färm, J., andLataillade, J.L., “Dynamic Fracture Toughness Determined from Load-point Displacement,” EXPERIMENTAL MECHANICS,34,217–223 (1994).

    Article  Google Scholar 

  7. Follansbee, P.S. andFrantz, C., “Wave Propagation in the Split Hopkinson Pressure Bar,”J. Eng. Mat. Tech.,105,61–66 (1983).

    Google Scholar 

  8. Gorham, D.A. andWu, X.J., “An Empirical Method for Correcting Dispersion in Pressure Bar Measurements of Impact Stress,”Meas. Sci. Tech. 7,1227–1323 (1996).

    Article  Google Scholar 

  9. Wang, L., Labibes, K., Azari, Z., andPluvinage, G., “Generalization of Split Hopkinson Bar Technique to Use Viscoelastic Bars,”Int. J. Impact Eng.,15,669–686 (1994).

    Google Scholar 

  10. Zhao, H. andGary, G., “A Three Dimensional Analytical Solution of the Longitudinal Wave Propagation in an Infinite Linear Viscoelastic Cylindrical Bar. Application to Experimental Techniques,”J. Mech. Phys. Solids,43,1335–1348 (1995).

    MathSciNet  Google Scholar 

  11. Zhao, H., Gary, G., andKlepaczko, J. R., “On the Use of a Viscoelastic Split Hopkinson Pressure Bar,”Int. J. Impact Eng.,19,319–330 (1997).

    Google Scholar 

  12. Zhao, H. andGary, G., “A New Method for the Separation of Waves. Application to the SHPB Technique for an Unlimited Duration of Measurement,”J. Mech. Phys. Solids,45,1185–1202 (1997).

    Google Scholar 

  13. Achenbach, J.D., Wave Propagation in Elastic Solids, North-Holland (1973).

  14. Lundberg, B. andBlanc, R. H., “Determination of Mechanical Material Properties from the Two-point Response of an Impacted Linearly Viscoelastic Rod Specimen,”J. Sound Vibration,126,97–108 (1988).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Mécanique Physique, Université Bordeaux 1, 33405, Taleuce Cedex, France

    C. Bacon (Senior Lecturer)

Authors
  1. C. Bacon
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

A part of this work has been performed in the Laboratoire Matériaux Endommagement Fiabilité of the Ecole Nationale Supérieure des Arts et Métiers de Bordeaux.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bacon, C. An experimental method for considering dispersion and attenuation in a viscoelastic Hopkinson bar. Experimental Mechanics 38, 242–249 (1998). https://doi.org/10.1007/BF02410385

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02410385

Key Words

Search

Navigation