Experimental investigation and numerical prediction on resistance of reactive powder concrete to multiple penetration
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摘要: 活性粉末混凝土（reactive powder concrete，RPC）具有超高的强度和优异的阻裂性能。为了研究RPC在多次冲击荷载下的损伤规律，采用25 mm口径滑膛炮对直径为600 mm、高600 mm的RPC圆柱形靶体进行了多次侵彻实验，得到了每次侵彻后靶体的破坏数据，并根据实验数据确定了Forrestal经验公式中的相关系数。基于K&C本构模型和现有RPC基本力学性能的实验数据，修正了K&C模型的强度面参数、损伤参数、状态方程参数、损伤演化模型以及应变率效应相关参数，系统地确定了RPC的K&C模型参数。采用LS-DYNA软件中的重启动功能模拟了弹体多次侵彻RPC靶体的破坏结果，模拟结果与实验结果基本一致，验证了模拟方法的有效性。对长2 200 mm、宽2 200 mm、高1 260 mm的RPC靶体抗侵彻实验进行了数值预测，得到了侵彻深度与弹速之间的关系、弹体贯穿靶体时的极限速度以及弹体侵彻过程中的峰值加速度。Abstract: Reactive powder concrete (RPC) has ultra-high strength and excellent crack resistance. To study the damage law of the RPC subjected to multiple impact loads, a 25 mm caliber smoothbore gun was used to penetrate the RPC cylindrical target with the diameter of 600 mm and the height of 600 mm. In addition, the experimental data of the target after each penetration was obtained, and the correlation coefficient in the Forrestal empirical formula was determined. Based on the K&C constitutive model and the existing experimental data of the RPC, the model parameters for the RPC were determined systematically by modifying the strength and surface parameters, damage parameters, equation-of-state parameters, damage evolution model, the strain rate effect. The restart function in the LS-DYNA software was used to simulate the damage results of the projectile repeatedly penetrating the RPC target. The simulation results are basically consistent with the experimental results, and the effectiveness of the simulation method is verified. Finally, the numerical prediction of the penetration resistance experiment of the RPC target with the length of 2 200 mm, the width of 2 200 mm, and the height of 1 260 mm was carried out. The relationship between the penetration depth and the projectile velocity, the minimum velocity of the projectile passing through the target and the peak acceleration during projectile penetration were obtained.
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图 3 高速摄影机记录的弹体撞击靶体过程
Figure 3. Process of the projectile impacting the targetrecorded by a high-speed camera
图 4 2%钢纤维掺量下不同强度RPC的Forrestal公式中的S*
Figure 4. S* in the Forrestal formula of RPC with differentcompressive strengths at 2% steel fiber content
图 8 混凝土和RPC三轴围压实验数据
Figure 8. Triaxial confining pressure experimental data of concrete and RPC
图 10 不同b3值对应的三轴拉伸应力应变曲线
Figure 10. Triaxial tension strain stress curvescorresponding to different b3 values
图 12 第1次侵彻RPC靶体的模拟结果
Figure 12. Simulation results of the first penetration of the RPC target
图 13 第2次侵彻RPC靶体的模拟结果
Figure 13. Simulation results of the second penetration of the RPC target
图 14 第3次侵彻RPC靶体的模拟结果
Figure 14. Simulation results of the third penetration of the RPC target
图 15 弹体与钢筋分布示意图（单位：mm）
Figure 15. Schematic diagram of the distribution of projectiles and reinforcement (unit: mm)
图 17 850 m/s弹速下的侵彻结果
Figure 17. Penetration results at the projectile velocity of 850 m/s
图 18 1 150 m/s弹速下的贯穿结果
Figure 18. Penetration results at the projectile velocity of 1 150 m/s
图 19 弹速与侵彻深度之间的关系
Figure 19. Relationship between projectile velocity and penetration depth
表 1 RPC材料配合比
Table 1. Mixture proportions of RPC
kg/m3 材料 胶凝材料 砂 减水剂 水 钢纤维 RPC 1 238 928 17.7 234.3 159 
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表 2 RPC基本力学性能参数
Table 2. Basic mechanical performance parameters of RPC
材料 fc/MPa ft /MPa E/GPa μ ρ/（g·cm−3） RPC 120 9.27 46.2 0.22 2.44
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表 3 靶体多次侵彻实验结果
Table 3. Experimental results of targets subjected to multiple penetrations
侵彻次数 v0/（m·s−1） h/mm S/cm2 H/mm N Wmax/mm 1 511.5 129.1 329.7 59.5 0 0 2 552.5 257.4 344.1 79.8 12 2 3 560.0 290.3 354.8 114.9 13 13
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表 4 弹体、钢箍以及钢筋材料模型参数
Table 4. Model parameters of projectile, steel culvert and steel bar material
材料 ρ/（kg·m−3） E/GPa μ σy/MPa 弹体 7 850 210 0.3 1 650 钢箍/钢筋 7 800 210 0.3 300
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表 5 损伤演化函数η(λ)
Table 5. Damage evolution function η(λ)
λ η λ η 0 0 4.0×10−6 0.51 2.7×10−5 0.62 6.7×10−4 0.37 6.8×10−5 0.92 1.2×10−3 0.27 8.0×10−5 0.99 2.0×10−3 0.20 1.0×10−4 1.00 5.5×10−3 0.10 1.4×10−4 0.96 1.6×10−2 0 2.6×10−4 0.66
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表 6 活性粉末混凝土的K&C模型应变率效应特征点取值
Table 6. K&C model strain rate characteristic points of reactive powder concrete
$\dot \varepsilon/{\rm{s}^{-1} }$ $\psi $ $\dot \varepsilon/{\rm{s}^{-1} }$ $\psi $ $\dot \varepsilon/{\rm{s}^{-1} }$ $\psi $ –30 000 9.97 –10 1.27 –1×10–4 1.07 –4 782 9.97 –3 1.24 –1×10–5 1.03 –1 000 5.41 –1 1.22 0 1.00 –300 3.45 –0.1 1.18 30 1.00 –100 2.29 –0.01 1.14 265 2.94 –25 1.28 –1×10–3 1.11 30 000 2.94
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表 7 RPC的K&C模型8号状态方程参数
Table 7. Parameters of No. 8 equation of state in the K&C model of RPC
εV εV1 εV2 εV3 εV4 εV5 εV6 εV7 εV8 εV9 εV10 0 0.0015 0.0043 0.0101 0.0305 0.0513 0.0726 0.0943 0.174 0.208 σV/GPa σV1 σV2 σV3 σV4 σV5 σV6 σV7 σV8 σV9 σV10 0 0.041 0.094 0.292 0.881 1.622 2.511 3.573 8.714 11.579 Kav/GPa Kav1 Kav2 Kav3 Kav4 Kav5 Kav6 Kav7 Kav8 Kav9 Kav10 27.5 27.5 27.885 29.288 34.843 40.425 45.980 50.186 112.915 137.5
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