Numerical simulation on ground shock waves induced by hypervelocity penetration of a projectile into a limestone target
-
摘要: 为探究超高速动能武器的对地破坏效应及其影响因素，采用数值模拟方法对弹体超高速侵彻的地冲击规律进行了研究。首先，基于石灰岩静动态力学性能实验数据对材料模型参数进行了标定，并对已有弹体大范围着速侵彻石灰岩靶体进行了模拟，验证了所采用材料模型和数值模拟方法的合理性。随后，开展了钨合金长杆弹超高速侵彻石灰岩靶体的数值模拟，细致分析了地冲击传播的现象和机理：弹体超高速侵彻靶体时，弹靶交界面处会产生瞬时高压，并以应力波的形式在靶体中传播，对靶体内部造成破坏，且当弹体初速度高于3.0 km/s时，地冲击显著增强。最后，进一步研究了不同弹靶参数对地冲击的影响，发现从相对深度来看，弹体参数（弹体长径比、密度）对地冲击规律影响不大；而靶体特征特别是孔隙率对地冲击传播具有较大影响。Abstract: With the advancement of hypervelocity weapons such as the “Rods-from-God”, the damage and failure in targets induced by the hypervelocity penetrators have been a topic of current research, which is still not fully understood. To address this issue, numerical investigation was carried out on ground shock induced by hypervelocity penetration of projectiles into limestone targets. As the material model and corresponding parameters are crucial for the accurate numerical predictions, the parameters for the p-α equation of state and the Kong-Fang material model recently proposed to describe the limestone were firstly calibrated based on a large amount of dynamic tests. The smooth particle hydrodynamics (SPH) method was employed for simulating the target and the axisymmetric numerical model was used to improve the computational efficiency. The calibrated parameters and numerical algorithm were validated by numerically simulating a series of penetration tests on limestone targets with a broad range of striking velocities. Then, based on the validated numerical model, the penetration of long-rod tungsten projectile into a limestone target was simulated and the mechanism of the corresponding ground shock was discussed. It was found that a high pressure in the target was induced by the hypervelocity impact of the projectile, which then propagated into the target as a stress wave, leading to the damage and failure in the target. The induced ground shock wave increased with the increase of the initial projectile velocity, especially when the initial projectile velocity is over 3.0 km/s. Finally, parametric study was conducted to investigate the effects of the parameters related to the projectiles and targets on the ground shock wave. The parameters related to the projectiles, for example, the length-to-diameter ratio and density, which can influence on the damage area of the targets by influencing the depth of penetration, has limited influence on the ground shock wave from the view of the relative depth (the ratio of the depth to the penetration depth). While the target parameters, especially the porosity which can affect the wave propagation, have a great effect on the ground shock wave.
-
Key words:
- hypervelocity penetration /
- ground shock wave /
- limestone /
- material model
-
图 1 最大强度面模型与实验数据的拟合
Figure 1. Fitting of the maximum strength surface model to the experimental data
图 2 石灰岩应力-应变曲线的数值模拟结果与实验数据的对比
Figure 2. Comparison of stress-strain curves of limestone between experimental data and numerical simulation
图 3 石灰岩动态强度增强因子随应变率的变化曲线
Figure 3. Changes of the dynamic increase factors with strain rate for limestone
图 4 石灰岩状态方程曲线与实验数据的拟合
Figure 4. Equation of state of limestone fitted to experimental data
图 5 数值模拟的侵彻深度与实验数据的对比
Figure 5. Simulated depths of penetration at different initial projectile velocities compared with experimental data
图 7 数值模拟得到不同撞击速度下的的侵彻深度
Figure 7. Simulated depths of penetration at different initial projectile velocities
图 8 超高速侵彻过程中的破坏现象及压力波传播
Figure 8. Damage and pressure wave propagation in the target during hypervelocity penetration
图 10 不同弹体初速度下应力峰值随深度的变化趋势
Figure 10. Change of peak stress with depth at different initial projectile velocities
图 11 侵彻深度与弹体长径比的关系（弹径不变）
Figure 11. Depth of penetration versus length-to-diameter ratio at a constant projectile diameter
图 14 不同孔隙率岩石材料的状态方程
Figure 14. Equations of state for limestones with different porosities
表 1 石灰岩的强度模型参数
Table 1. Parameters of the strength surface models for limestone
最大强度面 残余强度面 屈服强度面 损伤参数 a1 a2 a3 a1y a2y λm 0.877 0.022 0.80 0.890 0.046 3×10−5 
下载: 导出CSV
表 2 石灰岩的动态强度增强因子参数
Table 2. Parameters for dynamic increase factors of limestone
动态强度增强因子 Fm Wx S Wy DIFC 9 1.8 1.2 5.0 DIFT 10 1.6 1.6 5.5
下载: 导出CSV
表 3 石灰岩的状态方程参数
Table 3. Equation of state parameters for limestone
pcrush/MPa plock/GPa n A1/GPa A2/GPa A3/GPa 100 1.44 3 22.53 –175.0 495.0
下载: 导出CSV
表 4 不同弹体密度情况下的侵彻深度
Table 4. Depths of penetration at different projectile densities
材料 ρs/（kg∙m−3） （ρs/ρt）1/2 hp/m 铝 2785 1.10 2.58 钢 7830 1.85 4.69 钨 17000 2.73 6.20
下载: 导出CSV
-
[1] KONG X Z, WU H, FANG Q, et al. Projectile penetration into mortar targets with a broad range of striking velocities: test and analyses [J]. International Journal of Impact Engineering, 2017, 106: 18–29. DOI: 10.1016/j.ijimpeng.2017.02.022. [2] 钱秉文, 周刚, 李进, 等. 钨合金柱形弹超高速撞击水泥砂浆靶的侵彻深度研究 [J]. 爆炸与冲击, 2019, 39(8): 083301. DOI: 10.11883/bzycj-2019-0141.QIAN B W, ZHOU G, LI J, et al. Penetration depth of hypervelocity tungsten alloy projectile penetrating concrete target [J]. Explosion and Shock Waves, 2019, 39(8): 083301. DOI: 10.11883/bzycj-2019-0141. [3] 王杰, 武海军, 杨荷, 等. 高速/超高速侵彻半无限靶研究进展 [J]. 兵工学报, 2017, 38(S1): 73–88.WANG J, WU H J, YANG H, et al. Research progress in penetration of projectiles into semi-infinite targets at high-velocity/hypervelocity [J]. Acta Armamentarii, 2017, 38(S1): 73–88. [4] 李争, 刘元雪, 胡明, 等. “上帝之杖”天基动能武器毁伤效应评估 [J]. 振动与冲击, 2016, 35(18): 159–164. DOI: 10.13465/j.cnki.jvs.2016.14.026.LI Z, LIU Y X, HU M, et al. Damage effect evaluation of God stick space-based kinetic energy weapons [J]. Journal of Vibration and Shock, 2016, 35(18): 159–164. DOI: 10.13465/j.cnki.jvs.2016.14.026. [5] POELCHAU M H, KENKMANN T, THOMA K, et al. The MEMIN research unit: scaling impact cratering experiments in porous sandstones [J]. Meteoritics and Planetary Science, 2013, 48(1): 8–22. DOI: 10.1111/maps.12016. [6] 李干, 宋春明, 邱艳宇, 等. 超高速弹对花岗岩侵彻深度逆减现象的理论与实验研究 [J]. 岩石力学与工程学报, 2018, 37(1): 60–66. DOI: 10.13722/j.cnki.jrme.2017.0584.LI G, SONG C M, QIU Y Y, et al. Theoretical and experimental studies on the phenomenon of reduction in penetration depth of hyper-velocity projectiles into granite [J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(1): 60–66. DOI: 10.13722/j.cnki.jrme.2017.0584. [7] 钱秉文, 周刚, 李进, 等. 钨合金弹体超高速撞击混凝土靶成坑特性研究 [J]. 北京理工大学学报, 2018, 38(10): 1012–1017. DOI: 10.15918/j.tbit1001-0645.2018.10.004.QIAN B W, ZHOU G, LI J, et al. Study of the crater produced by hypervelocity tungsten alloy projectile into concrete target [J]. Transactions of Beijing Institute of Technology, 2018, 38(10): 1012–1017. DOI: 10.15918/j.tbit1001-0645.2018.10.004. [8] 孔祥振, 方秦, 吴昊, 等. 长杆弹超高速侵彻半无限靶理论模型的对比分析与讨论 [J]. 振动与冲击, 2017, 36(20): 37–43. DOI: 10.13465/j.cnki.jvs.2017.20.007.KONG X Z, FANG Q, WU H, et al. Comparisons of long rod high velocity penetration models for semi-infinite targets [J]. Journal of Vibration and Shock, 2017, 36(20): 37–43. DOI: 10.13465/j.cnki.jvs.2017.20.007. [9] KONG X Z, WU H, FANG Q, et al. Rigid and eroding projectile penetration into concrete targets based on an extended dynamic cavity expansion model [J]. International Journal of Impact Engineering, 2017, 100: 13–22. DOI: 10.1016/ j.ijimpeng.2016.10.005. [10] ANTOUN T H, GLENN L A, WALTON O R, et al. Simulation of hypervelocity penetration in limestone [J]. International Journal of Impact Engineering, 2006, 33: 45–52. DOI: 10.1016/j.ijimpeng.2006.09.009. [11] 邓国强, 杨秀敏. 超高速武器对地打击效应数值仿真 [J]. 科技导报, 2015, 33(16): 65–71. DOI: 10.3981/j.issn.1000-7857.2015.16.010.DENG G Q, YANG X M. Numerical simulation of damage effect of hyper velocity weapon on ground target [J]. Science and Technology Review, 2015, 33(16): 65–71. DOI: 10.3981/j.issn.1000-7857.2015.16.010. [12] 邓国强, 杨秀敏. 超高速武器流体侵彻与装药浅埋爆炸效应的等效方法 [J]. 防护工程, 2015, 37(6): 27–32.DENG G Q, YANG X M. Effect equivalent method between fluid penetration of hypervelocity weapon and shallow detonation of explosive [J]. Protective Engineering, 2015, 37(6): 27–32. [13] 王明洋, 岳松林, 李海波, 等. 超高速弹撞击岩石的地冲击效应等效计算 [J]. 岩石力学与工程学报, 2018, 37(12): 2655–2663. DOI: 10.13722/j.cnki.jrme.2018.0473.WANG M Y, YUE S L, LI H B, et al. An equivalent calculation method of ground shock effects of hypervelocity projectile striking on rock [J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(12): 2655–2663. DOI: 10.13722/j.cnki.jrme.2018.0473. [14] 方秦, 孔祥振, 吴昊, 等. 岩石Holmquist-Johnson-Cook模型参数的确定方法 [J]. 工程力学, 2014, 31(3): 197–204. DOI: 10.6052/j.issn.1000-4750.2012.10.0780.FANG Q, KONG X Z, WU H, et al. Determination of Holmquist-Johnson-Cook consitiutive model parameters of rock [J]. Engineering Mechanics, 2014, 31(3): 197–204. DOI: 10.6052/j.issn.1000-4750.2012.10.0780. [15] FOSSUM A F, SENSENY P E, PFEIFLE T W, et al. Experimental determination of probability distributions for parameters of a Salem limestone cap plasticity model [J]. Mechanics of Materials, 1995, 21(2): 119–137. DOI: 10.1016/0167-6636(95)00002-X. [16] KONG X Z, FANG Q, CHEN L, et al. A new material model for concrete subjected to intense dynamic loadings [J]. International Journal of Impact Engineering, 2018, 120: 60–78. DOI: 10.1016/j.ijimpeng.2018.05.006. [17] ZHANG S B, KONG X Z, FANG Q, et al. Numerical prediction of dynamic failure in concrete targets subjected to projectile impact by a modified Kong-Fang material model [J]. International Journal of Impact Engineering, 2020, 144: 103633. DOI: 10.1016/j.ijimpeng.2020.103633. [18] XU H, WEN H M. Semi-empirical equations for the dynamic strength enhancement of concrete-like materials [J]. International Journal of Impact Engineering, 2013, 60: 76–81. DOI: 10.1016/j.ijimpeng.2013.04.005. [19] FOSSUM A F, BRANNON R M. On a viscoplastic model for rocks with mechanism-dependent characteristic times [J]. Acta Geotechnica, 2006, 1(2): 89–106. DOI: 10.1007/s11440-006-0010-z. [20] FOSSUM A F. Rock penetration: finite element sensitivity and probabilistic modeling analyses [R]. Albuquerque, New Mexico: Sandia National Laboratories, 2004: 13–31. [21] WALTON G, HEDAYAT A, KIM E, et al. Post-yield strength and dilatancy evolution across the brittle-ductile transition in Indiana limestone [J]. Rock Mechanics and Rock Engineering, 2017, 50(7): 1691–1710. DOI: 10.1007/s00603-017-1195-1. [22] FREW D J, FORRESTAL M J, CHEN W. A split Hopkinson pressure bar technique to determine compressive stress-strain data for rock materials [J]. Experimental Mechanics, 2001, 41(1): 40–46. DOI: 10.1007/BF02323102. [23] CHAKRABORTY T, MISHRA S, LOUKUS J, et al. Characterization of three Himalayan rocks using a split Hopkinson pressure bar [J]. International Journal of Rock Mechanics and Mining Sciences, 2016, 85: 112–118. DOI: 10.1016/ j.ijrmms.2016.03.005. [24] KHAN A S, IRANI F K. An experimental study of stress wave transmission at a metallic-rock interface and dynamic tensile failure of sandstone, limestone, and granite [J]. Mechanics of Materials, 1987, 6(4): 285–292. DOI: 10.1016/0167-6636(87)90027-5. [25] KUBOTA S, OGATA Y, WADA Y, et al. Estimation of dynamic tensile strength of sandstone [J]. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(3): 397–406. DOI: 10.1016/j.ijrmms.2007.07.003. [26] WANG Q Z, LI W, XIE H P. Dynamic split tensile test of flattened Brazilian disc of rock with SHPB setup [J]. Mechanics of Materials, 2009, 41(3): 252–260. DOI: 10.1016/j.mechmat.2008.10.004. [27] CHO S H, OGATA Y, KANEKO K. Strain-rate dependency of the dynamic tensile strength of rock [J]. International Journal of Rock Mechanics and Mining Sciences, 2003, 40(5): 763–777. DOI: 10.1016/S1365-1609(03)00072-8. [28] HERRMANN W. Constitutive equation for the dynamic compaction of ductile porous materials [J]. Journal of Applied Physics, 1969, 40(6): 2490–2499. DOI: 10.1063/1.1658021. [29] HEARD H C, ABEY A E, BONNER B P. High pressure mechanical properties of Indiana limestone: UCID-16501 [R]. USA: California University, Lawrence Livermore National Laboratory, 1974. [30] LARSON D B, ANDERSON G D. Plane shock wave studies of porous geologic media [J]. Journal of Geophysical Research: Solid Earth, 1979, 84(B9): 4592–4600. DOI: 10.1029/JB084iB09p04592. [31] MURRI W J, SMITH C W, MAHRER K D. Equation of state of rocks: PYU-1883 [R]. USA: Stanford Research Institute, 1974. [32] FREW D J, FORRESTAL M J, HANCHAK S J. Penetration experiments with limestone targets and ogive-nose steel projectiles [J]. Journal of Applied Mechanics, 2000, 67(4): 841–845. DOI: 10.1115/1.1331283. [33] MCFARLAND C, PAPADOS P, GILTRUD M. Hypervelocity impact penetration mechanics [J]. International Journal of Impact Engineering, 2008, 35(12): 1654–1660. DOI: 10.1016/j.ijimpeng.2008.07.080. [34] STEINBERG D J, COCHRAN S G, GUINAN M W. A constitutive model for metals applicable at high strain rate [J]. Journal of Applied Mechanics, 1980, 51(3): 1498–1504. DOI: 10.1063/1.327799. [35] 杜成成. 应力波在混凝土中传播特性及结构特征参数监测研究 [D]. 哈尔滨: 哈尔滨工业大学, 2018: 49–77.DU C C. Research on transmission properties of stress waves in concrete and monitoring of structural characteristic parameters [D]. Harbin: Harbin Institute of Technology, 2018: 49–77. -
计量
- 文章访问数: 431
- HTML全文浏览量: 587
- PDF下载量: 222
- 被引次数: 0