Research on penetration depth of projectiles into ultra-high performance concrete targets
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摘要: 为了评估超高性能混凝土（UHPC）的抗侵彻性能，对UHPC靶板进行了侵彻试验与数值模拟。首先，利用
$\varnothing $ 35 mm火炮对抗压强度为160 MPa的UHPC靶板开展了216~345 m/s速度下的弹体侵彻试验，结果表明：随着弹体速度的增加，侵彻深度与开坑直径皆有明显增加。随后在数值模拟过程中，确立了UHPC的RHT材料模型参数，为了验证材料模型的有效性，采用单轴压缩与霍普金森压杆试验结果对三维有限元模型进行了验证，模拟结果与实验结果吻合良好，表明参数选取科学合理。最后，对弹体侵彻UHPC的过程进行数值模拟，参数化分析了UHPC抗压强度、弹体质量、侵彻速度、弹径、弹头形状对UHPC侵彻深度的影响，并据此推导出弹体对UHPC侵彻深度计算公式。Abstract: Aiming to evaluate the penetration resistance of the ultra high performance concrete (UHPC) target, both penetration tests and numerical simulations were carried out on UHPC targets. Firstly, the$\varnothing $ 35 mm gun was used to carry out a series of penetration tests on the C160 UHPC with striking velocities varying from 216 m/s to 345 m/s. The test results show that with the increase of projectile velocity, the penetration depth and crater diameter increase obviously. Besides, UHPC notably decreased the damage to targets caused by the projectile, efficiently reduced the penetration depth and regarding crater damage and crack propagation, which was superior to ordinary concrete in the performance against penetration. Then, 3D finite element models were established and the corresponding numerical simulations were carried out. In the process of numerical simulation, the key parameters of the RHT model for UHPC was determined. In order to verify the accuracy of the RHT material model, uniaxial compressive and split Hopkinson pressure bar (SHPB) testing results are used to validate 3D finite element material model. The numerical simulated results exhibited fair agreement with the test data, these observations demonstrated the applicability and validity of the calibrated RHT model. Finally, with the validated RHT material model, parametric studies were further conducted to explore the effect of uniaxial compressive strength of UHPC, projectile mass, projectile striking velocity, projectile diameter and projectile caliber-radius-head ratio on the final depth of penetration values of UHPC targets. Moreover, an empirical formula to predict the depth of penetration is derived according to the numerical simulated data, which can provide a reference for the design and evaluation of the UHPC protective structures against projectile penetrations.-
Key words:
- penetration /
- UHPC /
- CRH /
- RHT model
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图 9 单轴压缩与SHPB实验有限元模型
Figure 9. Finite element model for uniaxial compression and SHPB test
图 12 弹体侵彻UHPC有限元模型
Figure 12. The finite element model for the projectile impacting the UHPC target
图 13 不同侵彻速度下靶板破坏情况的试验与数值模拟对比
Figure 13. Comparison of target damage between the experiment and the numerical simulation at different velocities
图 16 弹头形状系数ϕ对侵彻深度的影响
Figure 16. Depth of penetration versus shape parameter of projectile ϕ
图 18 抗压强度对侵彻深度的影响
Figure 18. Depth of penetration versus various compressive strength of concrete
表 1 UHPC配合比
Table 1. Mixture design of UHPC
kg 水泥 石英砂 石英粉 硅灰 粉煤灰 钢纤维 水 减水剂 666 1065 160 160 80 157 135 6.7 
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表 2 钢纤维参数
Table 2. Parameters of steel fiber
直径/mm 长度/mm 拉伸强度/MPa 弹性模量/GPa 密度/(kg·m−3) 0.2±0.02 13±1.3 2000±300 200 7800
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表 3 侵彻试验结果
Table 3. Penetration tests data
试验 M/kg v/(m·s−1) h/mm h/d dc/mm dc/d 1# 1.001 216.2 145 4.83 200 6.67 2# 1.004 216.7 132 4.40 155 5.17 3# 1.000 226.9 147 4.90 220 7.33 4# 0.999 292.0 194 6.47 250 8.33 5# 1.003 304.1 203 6.77 200 6.67 6# 1.001 308.7 199 6.63 300 10.00 7# 0.999 313.2 199 6.63 300 10.00 8# 1.003 345.4 227 7.57 320 10.67 注：M为弹体质量，v为着靶速度，h为侵彻深度，d为弹体直径，dc为开坑直径。
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表 4 UHPC的RHT模型参数
Table 4. RHT model parameters of UHPC
ρ/(kg·m−3) G/GPa fc/MPa B1 B2 T1/GPa T2 A ${\dot \varepsilon ^{\text{c}}}$/s−1 ${\dot \varepsilon ^{\text{t}}}$/s−1 $\dot \varepsilon _{\text{0}}^{\text{c}}$/s−1 $\dot \varepsilon _{\text{0}}^{\text{t}}$/s−1 2450 18.5 160 1.22 1.22 44 0 1.6 3.0×1025 3.0×1025 3.0×10−5 3.0×10−6 pel/MPa $g_{\text{c}}^{\text{*}}$ $g_{\text{t}}^{\text{*}}$ $\xi $ D1 $\varepsilon _{\text{p}}^{\text{m}}$ Af nf A1/GPa A2/GPa A3/GPa βc 53.3 0.53 0.7 0.67 0.04 0.008 1.75 0.52 44 49.38 11.28 0.0125 βt B N D2 Q0 n $f_{\text{t}}^{\text{*}}$ $f_{\text{s}}^{\text{*}}$ pcom/GPa α0 0.0143 0.0105 4.0 1 0.681 0.61 0.0613 0.267 6 1.18 注：B1、B2为状态方程参数，A、n为失效面参数；$\dot \varepsilon ^{\text{c}}$为压缩失效应变率，${\dot \varepsilon ^{\text{t}}}$为拉伸失效应变率，$\dot \varepsilon _{\text{0}}^{\text{c}}$为参考压缩应变率，$\dot \varepsilon _{\text{0}}^{\text{t}}$为参考拉伸应变率，$g_{\text{c}}^{\text{*}}$为压缩屈服面参数，$g_{\text{t}}^{\text{*}}$为拉伸屈服面参数，$\xi $为剪切模量缩减系数；${D_1}$、${D_2}$为损伤参数；$\varepsilon _{\text{p}}^{\text{m}}$为最小失效应变，${A_{\text{f}}}$、${n_{\text{f}}}$为残余应力面参数，${\beta _{\text{c}}}$为压缩应变率指数，${\beta _{\text{t}}}$为拉伸应变率指数，B为罗德角相关系数，N为孔隙度指数，${Q_0}$为拉压子午比参数，${p_{{\text{com}}}}$为孔隙完全压实时压力，${\alpha _0}$为初始孔隙度。
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表 5 数值模拟与试验结果对比
Table 5. Comparison of experimental and numerical results
试验 弹速/
(m·s−1)侵彻深度/mm 深度
误差/%开坑直径/mm 直径
误差/%试验 计算 试验 计算 1 216.2 145 134 2.9 200 210 5.0 4 294.0 209 194 5.0 250 265 6.0 9 345.4 227 243 7.0 320 300 6.3
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表 6 数值模拟侵彻深度
Table 6. numerical simulated penetration depth
工况 fc/MPa ϕ v/(m·s−1) M/kg d/mm h/mm 1 160 10 200 1.0 30 134 2 300 209 3 350 245 4 400 288 5 450 330 6 500 370 7 550 410 8 160 10 300 0.25 30 78 9 0.5 110 10 1.0 209 11 1.5 245 12 2.0 350 13 2.5 386 14 3.0 422 15 160 4 300 1.0 30 142 16 6 161 17 8 175 18 10 209 19 12 215 20 160 10 300 1.0 18 335 21 24 239 22 30 209 23 36 162 24 42 138 25 35 10 300 1.0 30 360 26 60 270 27 90 255 28 140 211 29 160 209
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