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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2019, Vol. 13 Issue (5) : 1120-1137
An investigation of ballistic response of reinforced and sandwich concrete panels using computational techniques
Sonny Astani Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, CA 90007, USA
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Structural performance of nuclear containment structures and power plant facilities is of critical importance for public safety. The performance of concrete in a high-speed hard projectile impact is a complex problem due to a combination of multiple failure modes including brittle tensile fracture, crushing, and spalling. In this study, reinforced concrete (RC) and steel-concrete-steel sandwich (SCSS) panels are investigated under high-speed hard projectile impact. Two modeling techniques, smoothed particle hydrodynamics (SPH) and conventional finite element (FE) analysis with element erosion are used. Penetration depth and global deformation are compared between doubly RC and SCSS panels in order to identify the advantages of the presence of steel plates over the reinforcement layers. A parametric analysis of the front and rear plate thicknesses of the SCSS configuration showed that the SCSS panel with a thick front plate has the best performance in controlling the hard projectile. While a thick rear plate is effective in the case of a large and soft projectile as the plate reduces the rear deformation. The effects of the impact angle and impact velocity are also considered. It was observed that the impact angle for the flat nose missile is critical and the front steel plate is effective in minimizing penetration depth.

Keywords concrete panels      projectile impact      finite element modeling      smoothed particle hydrodynamics      strain rate effect     
Corresponding Authors: Bora GENCTURK   
Just Accepted Date: 24 May 2019   Online First Date: 26 June 2019    Issue Date: 11 September 2019
 Cite this article:   
Mohammad HANIFEHZADEH,Bora GENCTURK. An investigation of ballistic response of reinforced and sandwich concrete panels using computational techniques[J]. Front. Struct. Civ. Eng., 2019, 13(5): 1120-1137.
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Fig.1  Cross-sectional view of the panels (a) SCSS; (b) RC
parameter value
concrete strength (MPa) 23
rear plate thickness (mm) 32
front plate thickness (mm) 19
concrete block thickness (mm) 679
concrete block width (mm) 2000
concrete block length (mm) 2000
Tab.1  Geometry and material properties of the experiment [30]
part element type No.of elements
missile C3DR 345
front plate1 C3DR 40000
rear plate1 C3DR 12800
concrete core C3DR 124400
reinforcement2 T3D2 4400
impact area PC3D 300000
Tab.2  Summary of FE used in modeling
Fig.2  Meshing of the SCSS configuration. The concrete block has the same mesh density in the RC configuration
parameter notation value
dilation angle Ψ 38
flow potential eccentricity 0.1
biaxial/uniaxial compression plastic stress ratio fb0/fc 1.16
second stress invariant ratio K 0.667
viscosity parameter µ 0.0001
Tab.3  The parameters of the CDP model [29]
Fig.3  Uniaxial stress-strain behavior for 23 MPa concrete in (a) compression; (b) tension
parameter value
modulus of elasticity (MPa) Ec=5500f c'
tensile strength (MPa) ft=0.1 fc'
strain at maximum compressive stress 0.002
Poisson’s ratio 0.19
density (kg/m3) 2400
Tab.4  Concrete properties
part yield strength fy (MPa) Young’s modulus Es (GPa) yield strain ey ultimate stress fu (MPa) post-yield stiffness Eu (GPa) ultimate strain eu dynamic yield strength fyd (MPa)
reinforcement 475 190 0.002 751 18 0.12 688
plate 356 181 0.002 501 17 0.24 587
Tab.5  Material properties of steel plates and rebar
Fig.4  Stress-strain curve for steel (a) reinforcement; (b) plate
case number of elements min. concrete element size (mm) No. of elements through depth penetration depth (mm) rear deformation (mm)
fine 124,000 20 34 482 34
moderate 106,000 25 27 475 34
coarse 89,000 30 22 470 31
Tab.6  Results of mesh sensitivity study
Fig.5  An example plot of artificial strain energy (ASE) to internal energy (IE) ratio
Fig.6  Conventional FE simulation results for (a) side view; (b) isometric view. Damage varies between zero and unity for no and complete damage, respectively
Fig.7  Reaction force time history
Fig.8  SPH model (a) improved boundary conditions; (b) compressive damage. In part (b), damage varies between zero and unity for no and complete damage, respectively
parameter experiment conventional FE method SPH method
penetration depth (mm) 504 482 516
rear displacement (mm) 43 34 41
Tab.7  Comparison of experimental results from penetration tests on the SCSS panel [30] with the experimental data
Fig.9  Equivalent plastic strain, PEEQ, at (a) 5 ms; (b) 15 ms; (c) 30 ms
parameter notation US customary converted SI
penetration depth X 1 inch 25.4 mm
impact velocity V 1 ft/s 304.8 mm/s
projectile diameter d 1 inch 25.4 mm
projectile weight W 1 lb 0.454 kg
Tab.8  Input parameters for empirical models and unit conversion factors
Fig.10  Comparison between the empirical equations and the conventional FE model
case thickness (mm) penetration depth (mm) rear deformation (mm)
front rear
1 19 32 482 34
2 25 25 276 43
3 32 19 239 45
Tab.9  Parametric analysis of the steel plate thicknesses
Fig.11  Rear plate displacement at the center
Fig.12  Velocity of the projectile
Fig.13  Penetration depth time history
case impact velocity (m/s) kinetic energy (kJ) penetration depth (mm) rear deformation (mm) residual velocity (m/s)
1 200 1,000 219 10 0
2 314 2,464 482 34 0
3 400 4,000 6721 116 0
4 500 6,250 6721 176 0
5 600 9,000 6721 NA2 130
6 800 16,000 6721 NA2 310
7 1000 25,000 6721 NA2 440
8 1200 36,000 6721 NA2 530
9 1500 56,250 6721 NA2 720
Tab.10  Parametric analysis of the kinetic energy of the projectile
Fig.14  Compressive damage and penetration depth for the projectile with (a) 200 m/s; (b) 600 m/s impact velocity. Damage varies between zero and unity for no and complete damage, respectively
Fig.15  Residual velocity of the projectile versus different initial velocities
case impact angle (deg.) penetration depth (mm) rear deformation (mm)
1 90 482 34
2 75 647 39
3 60 523 23
4 45 324 17
5 30 74 3
6 15 0 1
Tab.11  Parametric analysis of the impact angle
Fig.16  Compressive damage at different time steps for Case 5 with 0.4 ms time step. Damage varies between zero and unity for no and complete damage, respectively
Fig.17  (a) Tensile; (b) Compressive damage for Case 5 at t = 16 ms. Damage varies between zero and unity for no and complete damage, respectively
Fig.18  von Misses stress (MPa) in the front plate for Case 6
Fig.19  (a) Penetration depth, (b) rear deformation for different impact angles
Fig.20  (a) Tensile; (b) compressive damage at v= 0 m/s for v0 = 300 m/s. Damage varies between zero and unity for no and complete damage, respectively
Fig.21  Rear plate displacement at the center
velocity (m/s) kinetic energy (kJ) Max. rear deform.(mm) rebound velocity (m/s)
200 1000 8.3 9
300 2250 18.0 17
400 4000 31.9 22
600 9000 56.5 21
800 16000 78.9 23
Tab.12  Parametric analysis of the impact angle
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