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REVIEW ARTICLES

Hopkinson bar experimental technique: A critical review

[+] Author and Article Information
Bazle A Gama

Department of Materials Science and Engineering, University of Delaware–Center for Composite Materials (UD-CCM), Newark DE 19716; gama@ccm.udel.edu

Sergey L Lopatnikov

Department of Civil and Environmental Engineering, University of Delaware–Center for Composite Materials (UD-CCM), Newark DE 19716; lopatnik@ccm.udel.edu

John W Gillespie

Department of Materials Science and Engineering, Department of Civil and Environmental Engineering, University of Delaware–Center for Composite Materials (UD-CCM), Newark DE 19716; gillespie@ccm.udel.edu

Appl. Mech. Rev. 57(4), 223-250 (Oct 12, 2004) (28 pages) doi:10.1115/1.1704626 History: Online October 12, 2004
Copyright © 2004 by ASME
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References

Figures

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Apparatus developed by Bertram Hopkinson for the measurement of pressure produced by the detonation of gun cotton. Reproduced from Fig. 12, Hopkinson 4, p 451.
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General arrangement of the apparatus developed by Davies. Reproduced from Fig. 1, Davies 5, p 382.
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Calculation of pressure in the Hopkinson Bar from displacement measurement at bar end. Reproduced from Fig. 12, Davies 5, p 403.
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Radial displacement data recorded and analyzed by Davies. Reproduced from Fig. 24, Davies 5, p 425.
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Axial displacement data recorded and analyzed by Davies. Reproduced from Fig. 29, Davies 5, p 438.
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Phase velocity c of extensional waves of wave-length Λ in cylindrical bars of radius a.ν=0.29,c1=velocity of dilatational waves, c2=velocity of distortional waves, cS=velocity of Raleigh surface waves. In terms of ν, c1/c0=[1−ν]/[(1+ν)⋅(1−2ν)],c2/c0=1/[2(1+ν)]. Reconstructed from the data provided in Table 11.1 and Fig. 13, Davies 5, pp 406–407.
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The variation of the displacements and the stresses over the cross section of a bar of radius a.xx̑=longitudinal stress; xȓ=shearing stress; rȓ=radial stress; ux=longitudinal displacement; ur=radial displacement; urp=radial displacement in distortionless bar. Reproduced from Fig. 19, Davies 5, p 418.
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Schematic of Kolsky’s apparatus. Reproduced from Fig. 1, Kolsky 6, p 678.
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Dynamic stress-strain behavior of Polythene. Reproduced from Fig. 8, Kolsky 6, p 693.
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Strain rate regimes and corresponding experimental techniques. Reproduced from 17; Fig. 1 and Table 1, p 427.
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Typical configurations of the Hopkinson Bar apparatus. Adopted from 18, Fig. 5, p 434.
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Techniques developed to use compression SHPB in testing specimens under tension. Reproduced from 18; Figs. 12 & 14, pp 438–439.
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Techniques developed to use Compression SHPB in testing specimens under double-notch shear. Reproduced from 23; Figs. 4 and 5, p 450.
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Additional methods using compression SHPB in testing specimens under shear. Reproduced from 23; Figs. 6 and 7, p 451.
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Recovery tension Hopkinson Bar setup. Reproduced from 25; Fig. 2, p 478.
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Triaxial SHPB testing technique. Reproduced from 26; Fig. 6, p 517.
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Strain gage signals obtained from a SHPB test of a 304L stainless steel specimen with a maraging steel bar. Reproduced from 14; Fig. 3, p 464.
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Traditional/modern 1D Hopkinson Bar analysis. Adopted from 14, Fig. 4, p 465.
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Conditions for planar bar-specimen interfaces. Numbers 1 and 2 represent IB-S and S-TB interfaces respectively. Symbol * denotes the location of interfaces when the specimen is deformed.
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Deformation of bar-specimen interfaces for small diameter acoustically hard specimens
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Test of stress equilibrium through 1-wave and 2-wave analysis. Reproduced from 14, Figs. 5 and 6, pp. 467–468.
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Comparison of a) rectangular-shaped pulse with b) ramp-shaped pulse obtained from the same length striker bar. Reproduced from 30, Fig. 8, p 501.
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Ceramic specimen design a) problem of indentation, impedance matched WC inserts, conical inserts, and dog-bone specimen b) steel ring lateral confinement for WC inserts. Reproduced from 30, Figs. 3 & 4, p 499.
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Normalized stress difference (stress non-equilibrium factor) between ceramic specimen ends as a function of number of wave reflections. Reproduced from 30, Fig. 2, p 498.
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Typical strain gage records of SHPB experiment
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Dimensionless phase velocity c/c0 as a function of a/Λ. Reproduced from 9, Table I, p 589.
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Dispersion of a trapezoidal pulse after traveling 0.61 m in a 4.6 mm diameter bar with ω0=3.021×104 s−1,c0=4830 m/s, and ν=0.29
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Comparison between Bancroft’s 10 and Davies’s 5 data, ν=0.29
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The first 50 Fourier coefficients for a trapezoidal function
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Location of time windows for a dispersion calculation. Reproduced from 31, Fig. 4, p 729.

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