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Modified spherical cavity-expansion model for projectile penetration into concrete targets

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Abstract

A modified spherical cavity-expansion model is developed in this paper. (1) We introduce a piecewise hyperbolic yield criterion suitable for pressure less than fc/3 to describe the mechanical behavior in the elastic region for the elastic–plastic response and modify the crack occurrence condition for the elastic–cracked–plastic response. (2) The hyperbolic yield criterion and a piecewise equation of state (EOS) are adopted for a better description of the plastic behavior of concrete material. Then, the modified model is validated by several projectile penetration tests in both the normal strength concrete (NSC) and ultra-high performance cement-based composite (UHPCC) targets. Finally, the hydrostatic pressure of the targets under rigid ogive-nosed projectile penetrations is found to be nearly within (0, 1.6 GPa), which usually exceeds the range that the shear strength-pressure test data covered. The influence of yield criterion on depth of penetration is discussed and it is recommended that the pressure should arrive at least 400 MPa in the related triaxial compression tests.

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Abbreviations

A, B, C :

Dimensionless resistance constants

B 1, B 2; C 1, C 2 :

Constants of integration

b 0, b 1, b 2 :

Constants in yield criterion

c, c 1 :

Interface velocities

c d :

Dilatational velocity

c p = (E/ρ 0)0.5 :

Reference velocity

d :

Projectile diameter

E :

Elastic modulus

f c :

Unconfined compressive strength

f t :

Uniaxial tensile strength

F = f t/f c :

Dimensionless tensile strength

K g :

General value of bulk modulus

m :

Projectile’s mass

N 1, N 2 :

Projectile nose shape coefficients

P :

Hydrostatic pressure

P g :

General intercept pressure in the equation of state (EOS)

r :

Radial Eulerian coordinate

S = σ r/f c :

Dimensionless radial stress

T = P/f c :

Dimensionless pressure

t :

Time

u :

Radial displacement

U = v/c :

Dimensionless particle velocity

v :

Particle velocity

V :

Projectile’s instantaneous velocity

V 0 :

Initial velocity of the projectile

V r :

Cavity-expansion velocity

x :

Instantaneous displacement

α = c 1/c d :

Dimensionless variable

β 1 = c 1/c p, β = c/c p :

Dimensionless interface velocities

ε = V r/c :

Dimensionless expansion velocity

μ :

Volumetric strain

\( \nu \) :

Poisson’s ratio

ξ 1 = r/(c 1 t), ξ = r/(ct):

Dimensionless coordinate

ρ :

Density of the concrete material

σ r :

Radial Cauchy stress

σ θ :

Circumferential Cauchy stress

ψ :

Caliber-radius-head of projectile

\( \bar{u}_{1} \) = u/(c 1 t):

Dimensionless variables

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Acknowledgements

This project was supported by the National Natural Science Foundations of China (Grants 51522813 and 51438003).

Author information

Authors and Affiliations

  1. College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, 410073, China

    Y. Peng

  2. Key Laboratory of Performance Evolution and Control for Engineering Structures, Tongji University, Shanghai, 200092, China

    H. Wu

  3. Research Institute of Structural Engineering and Disaster Reduction, College of Civil Engineering, Tongji University, Shanghai, 200092, China

    H. Wu

  4. State Key Laboratory for Disaster Prevention and Mitigation of Explosion and Impact, PLA Amy Engineering University, Nanjing, 210007, China

    Q. Fang & X. Z. Kong

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  1. Y. Peng
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  2. H. Wu
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  4. X. Z. Kong
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Correspondence to H. Wu.

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Peng, Y., Wu, H., Fang, Q. et al. Modified spherical cavity-expansion model for projectile penetration into concrete targets. Acta Mech. Sin. 35, 518–534 (2019). https://doi.org/10.1007/s10409-018-0815-7

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  • DOI: https://doi.org/10.1007/s10409-018-0815-7

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