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Instrumented Projectile Penetration Testing of Granular Materials

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Abstract

The results of a series of penetration experiments with cylindrical projectiles (diameter: 30 mm, length: 158 mm) of different tip geometries (hemispherical, conic and flat) impacting with approx. 380 m/s on cylindrical sand targets (diameter: 250 mm, length: 1 m) are presented. The projectiles are instrumented with an on-board data recorder system with acceleration sensor (G-Rec), allowing for in-situ measurement of the decelerations experienced during the impact and during the subsequent penetration process. During and after the acceleration stage inside the gun barrel, the velocities derived from the G-Rec data show a very good agreement with an independent reference velocity measurement obtained by a light barrier system. Immediately after the initial impact on the granular material (compacted sand for this study), the sensor signals indicate very strong amplitude oscillating decelerations in the range of 50,000 to 80,000 g. The measured penetration depth varied widely for identical conditions of projectile impact, using identical preparation procedures for the sand sample. Variables considered for the experimental program included projectile tip shape, initial sand compaction state, and projectile velocity. A data reduction procedure to obtain velocity and position information of the projectile while penetrating the sand assembly is presented, taking into account a constant value (offset) observed in the raw signals of G-Rec at the end of penetration process. The formation of a false tip of agglomerated quartz powder in front of the projectile was observed in all cases. The observed shape of the false tip (penetrator tip with comminuted sand) was found to be identical for all projectile tip shapes (flat, hemispherical, and conical) considered in this study. Initial examination results of the false tip using X-ray computed tomography are presented.

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Acknowledgments

The authors gratefully acknowledge the support of the Defense Threat Reduction Agency (DTRA), Grant No: HDTRA1-12-1-0045

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Authors and Affiliations

  1. Fraunhofer-Institute for High-Speed Dynamics, Ernst-Mach-Institut, Eckerstraße 4, 79104, Freiburg, Germany

    C. Glößner, S. Moser, R. Külls, S. Heß, S. Nau & M. Salk

  2. Civil and Environmental Engineering Department, University of Tennessee, 851 Neyland Drive, Knoxville, TN, 37996-2503, USA

    D. Penumadu

  3. Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, UK

    N. Petrinic

Authors
  1. C. Glößner
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  2. S. Moser
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  3. R. Külls
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  4. S. Heß
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  5. S. Nau
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  6. M. Salk
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  7. D. Penumadu
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Corresponding author

Correspondence to D. Penumadu.

Appendix-1: Data Correction Procedure for G-Rec Sensor and Numerical Integration Scheme

Appendix-1: Data Correction Procedure for G-Rec Sensor and Numerical Integration Scheme

The short-term zero-shift is mathematically described by a decaying exponential function. Together with the constant offset the correction formula can be written as:

$$ {a}_{cor}(t)={a}_{meas}(t)-{A}_{const}-{A}_{exp}\cdot {e}^{-c\left(t-{t}_0\right)} $$

The correction was conducted with four of the data sets according to the following procedure:

  1. 1.

    From the raw data, estimate the point in time when the projectile stopped moving.

    • For all data sets tend = 165 ms was chosen.

  2. 2.

    Find the starting point of the deceleration phase.

    • For all data sets t0 = 153.5 ms was chosen.

  3. 3.

    Chose a value for c, such that the exponential term becomes small at tend.

    • For all data sets c = 400 1/s was chosen, which corresponds to a 1 % remainder at tend.

  4. 4.

    Subtract the offset Aconst at tend from the deceleration data.

    • This varied between 200 and 400 g.

  5. 5.

    Vary Aexp until the time-integral of the deceleration, i.e. the velocity, matches the impact velocity

    • This varied between 2000 and 4000 g.

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Glößner, C., Moser, S., Külls, R. et al. Instrumented Projectile Penetration Testing of Granular Materials. Exp Mech 57, 261–272 (2017). https://doi.org/10.1007/s11340-016-0228-0

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  • DOI: https://doi.org/10.1007/s11340-016-0228-0

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