Behavior of High-Strength and Ultrahigh-Performance Concrete Targets Subjected to Relatively Rigid Projectile Impact
Abstract
Introduction
Review of Existing Equations for Local Impact Load Resistance
Nose Shape Factor
Equations | Parameters |
---|---|
Modified NDRC (Kennedy 1976) | 0.72, 0.84, 1.0, and 1.14 for flat, blunt, hemispherical, and sharp, respectively |
Hughes (1984) | 1.0, 1.12, 1.26, and 1.39 for flat, blunt, hemispherical, and sharp, respectively |
Young (Sandia) (1997) | for ogive, |
for conical, and | |
for blunt | |
UMIST (Reid and Wen 2001) | 0.72, 0.84, 1.0, and 1.13 for flat, blunt, hemispherical, and sharp, respectively |
Li and Chen (2003) | for ogive nose |
for blunt/spherical nose | |
for conical nose | |
Hwang et al. (2017) | 2.0, 1.9, 1.55, and 0.9 for flat, hemispherical, ogive, and sharp, respectively, and these values are used to calculate the spalling energy |
1.0, 0.9, 0.7, and 0.2 for flat, hemispherical, ogive, and sharp, respectively, and these values are used to calculate the tunneling energy |
Note: Refer to Figs. 1(a–c) for notations.
Existing Equations for Penetration Depth
Experimental Program
Test Plan and Specimens
Material | Values of specimens for 35–150 MPa concretes | ||||
---|---|---|---|---|---|
(MPa) | 35 | 80 | 100 | 120 | 150 |
(%) | 42 | 18.8 | 14.9 | 13.5 | 20 |
(%) | 47 | 40 | 36 | 35 | — |
Water () | 160 | 150 | 140 | 130 | 196.9 |
Cement () | 210 | 400 | 470 | 432 | 1,287.8a |
Fine aggregates () | 826 | 578 | 484 | 473 | 866.4 |
Coarse aggregates () [maximum size (mm)] | 942 [25] | 882 [20] | 876 [20] | 892 [20] | — |
ZrSF () | — | 120 | 141 | 144 | — |
Fly ash () | 76 | — | — | — | — |
Slag powder () | 95 | 280 | 329 | 384 | — |
Superplasticizer () | — | 10 | 11.75 | 12 | 24.4 |
Air-entraining agent () | 3.05 | — | — | — | 0.9 |
Steel fibers () 16 mm and 20 mm | — | — | — | — | 39 and 78 |
(MPa) | 41 | 103 | 81 | 96 | 162 |
(MPa) | 5.5 | 8.46 | 7.84 | 8.37 | — |
(MPa) | 3.46 | 7.09 | 5.73 | 4.43 | 14.23 |
for 150 MPa | |||||
Density () | 2,330 | 2,421 | 2,464 | 2,426 | 2,406 |
Note: = specified compressive concrete strength; = measured compressive concrete strength; = measured flexural strength; = measured splitting tensile strength; = measured direct tensile strength; = water-binder ratio; = fine aggregate ratio; and ZrSF = zirconia silica fume.
Testing
Material Curing and Tests
Impact Tests
Test Results and Analysis
Material Test Results
Penetration Depth
Specimen | () | (mm) | () | ||||||
---|---|---|---|---|---|---|---|---|---|
41C-1C | 115 | 12.57 | 2.32 | 0.78 | 0.68 | 0.35 | 1.00 | 1.98 | 0.56 |
41C-2C | 114 | 13.07 | 2.43 | 0.81 | 0.71 | 0.37 | 1.05 | 2.08 | 0.59 |
41C-3C | 113 | 13.91 | 2.66 | 0.88 | 0.76 | 0.39 | 1.20 | 2.26 | 0.64 |
41C-4H | 119 | 14.07 | 2.21 | 0.86 | 0.79 | 0.37 | 1.10 | 2.57 | 0.59 |
41C-5H | 118 | 12.5 | 1.99 | 0.77 | 0.71 | 0.33 | 0.99 | 2.30 | 0.53 |
Average for C-series | 13.18 | 2.47 | 0.82 | 0.72 | 0.37 | 1.08 | 2.10 | 0.60 | |
Average for H-series | 13.29 | 2.10 | 0.82 | 0.75 | 0.35 | 1.04 | 2.43 | 0.56 | |
41C average | 13.22 | 2.32 | 0.82 | 0.73 | 0.36 | 1.07 | 2.24 | 0.58 | |
81C-1C | 116 | 9.33 | 1.67 | 0.68 | 0.56 | 0.30 | 0.79 | 2.20 | 0.50 |
81C-2C | 135 | 10.02 | 1.34 | 0.64 | 0.54 | 0.28 | 0.70 | 1.84 | 0.45 |
81C-3C | 131 | 10.7 | 1.51 | 0.70 | 0.59 | 0.31 | 0.78 | 2.06 | 0.49 |
81C-4H | 120 | 9.4 | 1.43 | 0.67 | 0.59 | 0.28 | 0.75 | 2.56 | 0.47 |
81C-5H | 133 | 11.41 | 1.44 | 0.75 | 0.67 | 0.31 | 0.81 | 2.64 | 0.50 |
81C-6H | 123 | 9.73 | 1.41 | 0.68 | 0.60 | 0.28 | 0.76 | 2.54 | 0.48 |
Average for C-series | 10.02 | 1.51 | 0.67 | 0.57 | 0.30 | 0.76 | 2.03 | 0.48 | |
Average for H-series | 10.18 | 1.43 | 0.70 | 0.62 | 0.29 | 0.77 | 2.58 | 0.50 | |
81C average | 10.10 | 1.47 | 0.69 | 0.59 | 0.29 | 0.77 | 2.31 | 0.48 | |
96C-1C | 111 | 9.49 | 1.87 | 0.65 | 0.55 | 0.29 | 0.82 | 2.12 | 0.47 |
96C-2C | 126 | 8.21 | 1.27 | 0.57 | 0.48 | 0.25 | 0.72 | 1.87 | 0.41 |
96C-3C | 129 | 10.08 | 1.48 | 0.67 | 0.56 | 0.29 | 0.84 | 2.10 | 0.48 |
96C-4H | 123 | 9.6 | 1.41 | 0.65 | 0.58 | 0.27 | 0.80 | 2.50 | 0.45 |
96C-5H | 117 | 10.44 | 1.68 | 0.78 | 0.67 | 0.33 | 0.97 | 3.19 | 0.55 |
96C-6H | 112 | 9.96 | 1.75 | 0.72 | 0.63 | 0.30 | 0.90 | 2.93 | 0.51 |
Average for C-series | 9.26 | 1.54 | 0.63 | 0.53 | 0.29 | 1.05 | 2.36 | 0.49 | |
Average for H-series | 10.00 | 1.61 | 0.72 | 0.63 | 0.30 | 0.89 | 2.87 | 0.48 | |
96C average | 9.63 | 1.36 | 0.67 | 0.58 | 0.29 | 0.84 | 2.45 | 0.48 | |
103C-1C | 114 | 7.83 | 1.47 | 0.62 | 0.50 | 0.27 | 1.02 | 2.31 | 0.47 |
103C-2C | 123 | 9.39 | 1.50 | 0.69 | 0.56 | 0.30 | 1.09 | 2.41 | 0.51 |
103C-3H | 125 | 9.4 | 1.40 | 0.71 | 0.61 | 0.30 | 1.01 | 3.02 | 0.50 |
103C-4H | 121 | 8.84 | 1.46 | 0.70 | 0.59 | 0.29 | 1.10 | 3.10 | 0.51 |
103C-5H | 135 | 9.59 | 1.39 | 0.71 | 0.62 | 0.30 | 1.09 | 3.01 | 0.50 |
Average for C-series | 8.61 | 1.48 | 0.65 | 0.53 | 0.29 | 1.05 | 2.36 | 0.49 | |
Average for H-series | 9.28 | 1.42 | 0.71 | 0.61 | 0.30 | 1.07 | 3.04 | 0.50 | |
103C average | 9.01 | 1.44 | 0.69 | 0.58 | 0.29 | 1.06 | 2.77 | 0.50 | |
162C-1C | 115 | 7.61 | 1.39 | 0.66 | 0.51 | 0.43 | 1.13 | 3.15 | 0.40 |
162C-2C | 117 | 8.32 | 1.47 | 0.71 | 0.56 | 0.47 | 1.20 | 3.34 | 0.42 |
162C-3C | 113 | 6.04 | 1.16 | 0.54 | 0.41 | 0.35 | 0.90 | 2.59 | 0.32 |
162C-4C | 123 | 7.57 | 1.21 | 0.62 | 0.49 | 0.41 | 1.01 | 2.80 | 0.36 |
162C-5H | 98 | 5.98 | 1.39 | 0.62 | 0.48 | 0.38 | 1.14 | 4.05 | 0.39 |
162C-6H | 106 | 6.02 | 1.18 | 0.57 | 0.46 | 0.37 | 0.88 | 3.50 | 0.33 |
162C-7H | 117 | 7.25 | 1.16 | 0.63 | 0.52 | 0.39 | 1.04 | 3.56 | 0.36 |
Average for C-series | 7.39 | 1.31 | 0.63 | 0.49 | 0.42 | 1.06 | 2.97 | 0.38 | |
Average for H-series | 6.42 | 1.24 | 0.61 | 0.49 | 0.38 | 1.02 | 3.70 | 0.36 | |
162C average | 6.97 | 1.28 | 0.62 | 0.49 | 0.40 | 1.04 | 3.28 | 0.36 | |
Average | 119 | — | — | 0.69 | 0.59 | 0.33 | 0.95 | 2.64 | 0.48 |
COV | — | — | — | 0.116 | 0.153 | 0.162 | 0.156 | 0.208 | 0.161 |
Note: Specimen ID indicates the following: 41C → measured concrete strength, 1 → specimen number, and C or H → conical or hemispherical nose; = measured penetration depth; = kinetic energy; and , , , , , and are predicted penetration depths using modified NDRC, Hughes, Li-Chen, Hwang, UMIST, and Young equations, respectively.
Projectile | (MPa) | (MPa) | (mm) | (kN) |
---|---|---|---|---|
Conical projectile | 41 | 44,404 | 13.18 | 12,451 |
81 | 62,311 | 10.02 | 10,115 | |
96 | 67,775 | 9.26 | 9,442 | |
103 | 70,220 | 8.61 | 8,457 | |
162 | 89,496 | 7.39 | 7,984 | |
Hemisphere projectile | 41 | 44,404 | 13.29 | 7,846 |
81 | 62,311 | 10.18 | 6,903 | |
96 | 67,775 | 10.00 | 7,145 | |
103 | 70,220 | 9.28 | 6,564 | |
162 | 89,496 | 6.42 | 4,506 |
Note: = measured compressive strength; = elastic modulus of concrete affected by strain rate; = measured penetration depth; and = calculated impact force.
Nose Shape Factors in Existing Equations
Penetration Analysis with Hertzian Contact Theory
Design Application
Summary and Conclusions
Data Availability Statement
Acknowledgments
References
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Cited by
- Gang-Kyu Park, MinJoo Lee, Namkon Lee, Gi-Joon Park, Sung-Wook Kim, Dynamic structural responses of high-performance fiber-reinforced cement composites panels subjected to high-velocity projectile impact loadings, Composite Structures, 10.1016/j.compstruct.2022.116581, 306, (116581), (2023).
- MinJoo Lee, Gang-Kyu Park, Sung-Wook Kim, Hyo-Gyoung Kwak, Damage characteristics of high-performance fiber-reinforced cement composites panels subjected to projectile impact, International Journal of Mechanical Sciences, 10.1016/j.ijmecsci.2021.106919, 214, (106919), (2022).