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Terminal depth of penetration of spherical projectiles in transparent granular media

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Abstract

A series of 80 penetration tests were performed to study the terminal depth of penetration into dry and saturated transparent synthetic sand. The transparent sand was made by matching the refractive index of granulated fused quartz with a pore fluid made of either sucrose or mineral oil. Tests were conducted by shooting spherical projectiles at speeds of up to 200 m/s into the transparent soil and recording the depth of penetration non-intrusively, when possible. Analysis using existing physical and empirical models was conducted to see how well these models describe the penetration event into fused quartz and to provide best fit parameters. Adjustments to published models have also been derived which result in adequate correlations to the experimental data.

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Abbreviations

\(e\) :

Void ratio

\(F\) :

Force on the projectile

\(M\) :

Mass

\(V\) :

Instantaneous velocity of the projectile

\(\rho \) :

Density of the penetrated medium

\(A\) :

Projectile frontal area

\(C\) :

Coefficient that plays role of drag in Newton’s third law

\(C_{D}\) :

Drag coefficient used in aerodynamics

\(C_{p}\) :

Drag coefficient used in Poncelet model

\(R\) :

Static strength term proportional to the yield strength of the material

\(B\) :

Viscous term

\(d\) :

Diameter

\(\rho _{p}\) :

Density of the projectile

\(\rho _{t}\) :

Total (bulk) density of the target

\(P\) :

Terminal depth of penetration

\(v_{o}\) :

Impact velocity

\(W\) :

Weight of the projectile

\(S\) :

Soil penetrability number in Young’s equation

N:

Nose performance coefficient in Young’s equation

CRH :

Caliber radius head

\(L_{n}\) :

Nose length

\(K_{s}\) :

Mass scaling term in Young’s equation

\(K_{s}^{\prime }\) :

Modified mass scaling term for use in Young’s equation

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Acknowledgments

The authors gratefully acknowledge the support of the Defense Threat Reduction Agency Grant No: HDTRA1- 10-1-0049 and The United States National Science Foundation Grant No: DGE 0741714. Fused quartz powder used in this investigation was manufactured by Mineral Technology Corporation (Mintec). Low Color Sucrose\(^\mathrm{TM}\) used to match the fused quartz was manufactured by Indiana Sugars. Krystol \(40^\mathrm{TM}\) and Puretol \(7^\mathrm{TM}\) used to match the fused quartz were manufactured by PetroCanada/Suncor. The high speed image in Fig. 1 was captured using a NAC HX-5 camera.

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Authors and Affiliations

  1. New Jersey Institute of Technology, Newark, NJ, USA

    Ivan L. Guzman

  2. Civil and Urban Engineering Department, NYU Polytechnic School of Engineering, Brooklyn, NY, 11201, USA

    Magued Iskander

  3. NYU Polytechnic School of Engineering, Brooklyn, NY, USA

    Stephan Bless

  4. NYU Polytechnic School of Engineering and Ningbo University, Ningbo, China

    Changguang Qi

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  1. Ivan L. Guzman
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  2. Magued Iskander
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Correspondence to Magued Iskander.

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Guzman, I.L., Iskander, M., Bless, S. et al. Terminal depth of penetration of spherical projectiles in transparent granular media. Granular Matter 16, 829–842 (2014). https://doi.org/10.1007/s10035-014-0528-y

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