Dynamic constitutive model of coral sand under blast loading
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摘要: 以珊瑚砂为主要覆盖域的岛礁在面临动力灾变时，确定岛礁工程抵抗极端冲击荷载的阈值至关重要，珊瑚砂的动态本构关系是防护工程设计的关键要素。本文中，根据SHPB实验和静态压缩实验的结果，提出了一种基于应变率强化规律确定珊瑚砂物态方程的方法，并确定了珊瑚砂动态本构模型的参数。分别基于流体弹塑性模型和Perzyna黏塑性帽盖模型，结合LS-DYNA有限元程序，通过对侵彻和爆炸的数值计算，验证了模型的适用性。基于建立的模型，对不同相对密实度的珊瑚砂开展了侵彻和爆炸数值计算，结果表明，密实度对爆炸波的衰减影响较大、对侵彻深度的影响较小。
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关键词:
- 珊瑚砂 /
- 动态本构 /
- LS-DYNA有限元程序 /
- 侵彻 /
- 爆炸
Abstract: Coral sand is widely distributed in the large area of reefs and lagoons in the South China Sea. During the construction of various projects on islands and reefs, the coral sand is extensively used as a local material resource. It is very important to determine the threshold of the reef engineering to resist extreme impact loads when the islands and reefs covered with coral sand was suffered from dynamic disasters such as penetration and explosion. The coral sand dynamic constitutive model is a key component for protection engineering design when engineering calculations are required. Based on the results of SHPB experiment and static compression experiment of coral sand from the previous works, a method was proposed to determine the equation of state of coral sand based on the law of strain rate strengthening effect by comparing the static compression curves and the dynamic compression curves. It has been proved that the average pressure of the compression curve can reach more than 100 MPa by using this fitting method.The parameters of the dynamic constitutive model of coral sand were determined through the processing of a lot of experiment results. Based on the hydrodynamic elasto-plastic model and the Perzyna viscoplastic cap model, combined with the LS-DYNA finite element program, the applicability of the dynamic constitutive models was verified by contrasting the numerical calculations and experimental results of the coral sand suffered from the projectile penetration and the blasting of explosive. According to the established model, numerical calculations of penetration and explosion in coral sand with different compactness levels were carried out using the hydrodynamic elasto-plastic model. The results show that the compactness levels of coral sand have a greater influence on the attenuation of the blasting wave and less on the penetration depth. This is because the poorly graded original coral sand has a smaller measurement difference between the maximum and minimum dry densities.-
Key words:
- coral sand /
- dynamic constitutive /
- LS-DYNA finite element program /
- penetration /
- explosion
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图 1 确定屈服参数的摩尔圆
Figure 1. Mohr’s circle geometry used to determine yield surface parameters
图 3 在不同相对密实度下平均压力与体应变的关系
Figure 3. Average pressure-volumetric strain curves under different compactness levels
图 6 侵彻计算模型网格划分（靶体为部分显示）
Figure 6. Finite element mesh of calculated model (target is partially displayed)
图 8 不同入射速度时速度与深度的关系
Figure 8. Velocity versus penetration depth at different initial velocities
图 9 珊瑚砂在不同时刻的压力场和弹丸产生的磨蚀区
Figure 9. Pressure fields of coral sand at diffident times and scratch area of projectile
图 10 不同压实密度时速度与深度的关系
Figure 10. Velocity versus penetration depth under different compactness levels
图 11 峰值压力的衰减
Figure 11. Calculated and experiment results of peak pressure attenuation
图 14 不同相对密度时爆炸峰值压力与比例距离的关系
Figure 14. Peak pressure versus scaled distance under different compactness levels
表 1 当
$D_{\rm r}=0.30 $ 时珊瑚砂的5#材料模型参数Table 1. Parameters of 5# constitutive model for coral sand when
$D_{\rm r}=0.30 $ ρ/（g·cm−3） G/MPa Ku/MPa a0/kPa2 a1/kPa a2 1.178 107.7 647.3 84.77 16.23 0.777 ln（V/V0） 0 0.02 0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 p/MPa 0 2.3 5.8 8.5 11.7 15.83 21.03 36.43 62.23 105.09 
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表 2 当
$D_{\rm r}=0.60 $ 时珊瑚砂的5#材料模型参数Table 2. Parameters of 5# constitutive model for coral sand when
$D_{\rm r}=0.60 $ ρ/（g·cm−3） G/MPa Ku/MPa a0/kPa2 a1/kPa a2 1.219 125.2 698.7 84.77 16.23 0.777 ln（V/V0） 0 0.02 0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 p/MPa 0 3.0 7.5 10.4 14.0 18.9 25.6 45.0 77.2 132.3
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表 3 当
$D_{\rm r}=0.90 $ 时珊瑚砂的5#材料模型参数Table 3. Parameters of 5# constitutive model for coral sand when
$D_{\rm r}=0.90 $ ρ/（g·cm−3） G/MPa Ku/MPa a0/kPa2 a1/kPa a2 1.260 158.9 717.2 84.77 16.23 0.777 ln（V/V0） 0 0.02 0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 p/MPa 0 3.66 8.43 10.87 14.51 19.56 26.48 46.89 82.18 141.09
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表 4 当
$D_{\rm r}=0.30 $ 时珊瑚砂Perzyna黏塑性帽盖模型参数Table 4. Perzyna viscoplastic cap model parameters of coral sand when
$D_{\rm r}=0.30 $ K/MPa G/MPa α/kPa β/MPa−1 γ/kPa θ T/kPa 125.2 101.1 32.5 2.207 165 0.416 1.2 W D/GPa−1 R X0/kPa η/μs−1 f0/GPa N 0.365 5.58 5.15 10 0.02 120 1.0
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