Penetration mechanism of a high-speed projectile into a shelter made of spherical aggregates
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摘要: 在钻地弹威慑之下，重要目标工事外覆盖遮弹层是常见加固和防护手段。硬质球形颗粒（以下简称颗粒）是常见的遮弹层组成结构。本文中将研究高速侵彻弹体与颗粒作用机理，分析遮弹效率的控制因素。首先，基于动态空腔膨胀理论，计及靶的自由面效应和颗粒强度差异，建立了靶对弹体侵彻阻力的表征模型。然后，采用弹靶分离计算方法，模拟并分析了斜侵彻含球形颗粒有限大高强混凝土时弹体的运动与变形，研究颗粒的强度、位置及尺寸对来袭弹侵彻行为的影响规律。结果表明，颗粒的遮弹作用主要取决于与其作用时弹体的姿态，其随颗粒位置变化无明显规律；颗粒强度越高，遮弹效果越好；颗粒半径从1倍到10倍弹径变化时，颗粒对弹体的作用机理从弹道偏转为主转变为弹道偏转与侵彻阻力增加两者耦合。因此，为达到良好的遮弹效果，单层球形颗粒密排遮弹层的颗粒半径建议在5倍弹体直径之上；若采用较小颗粒制作遮弹层，建议采用多层错排方式，且遮弹层厚度须在10倍弹径之上。Abstract: Under the threat of earth penetration weapons (EPWs), the protective fortification should be further enhanced. The bursting layer is commonly used to increase the protective strength of the fortification. A hard spherical aggregate (aggregate for short) is often used to construct the bursting layer. The mechanism of a high-speed projectile into the aggregate was studied, and the dominant factors were investigated in the present paper. Based on the dynamic spherical cavity expansion theory, the model for the drag force of the projectile was constructed considering the free surface effect of the target and the strength of the aggregate. Detaching the projectile response from the target, the resistant force of the target was loaded on the projectile surface as a force boundary. The deformation and movement of the projectile was numerically researched when it obliquely penetrated into the high-strength concrete target including aggregates. The influences of aggregate strength, location and dimensions upon the projectile response were investigated. It indicates that the sheltering effect of the aggregate is mainly dominated by the gesture of the projectile impacting on the aggregate. However, the variation of the gesture does not follow a distinct law. It is shown that the higher the strength of the aggregate, the better the sheltering effect of the aggregate. The main sheltering mechanism transforms from ballistic trajectory deflection into combination of ballistic trajectory deflection and augment of the drag force of the projectile, when the radius of the aggregate increases from 1 time of projectile diameter to 10 times. Based on the above analyses, for the bursting layer made of one layer, the diameter of the aggregate should be larger than 10 times of the projectile diameter. However, when the size of the aggregate decreases, the bursting layers should be constructed by multiple and staggered layers of aggregates with total layer thickness larger than 10 times of the projectile diameter, in order to achieve the effective sheltering effect.
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图 1 侵彻过程中混凝土靶空腔膨胀响应分区
Figure 1. Partition of a concrete target during penetration based on the dynamic cavity expansion model
图 2 非正侵彻弹体与靶自由面位置示意图
Figure 2. Scheme of a projectile obliquely penetrating into a target
图 3 自由面衰减函数随弹体表面质点离自由面距离的变化
Figure 3. Change of the discount factor of free-surface effect with the distance from the target free surface to the projectile surface
图 7 颗粒位置及强度变化时弹尖xy平面内运动轨迹
Figure 7. Trajectory of projectile nose tip in xy plane with variation of location and strength of aggregate
图 8 侵彻后弹体的等效塑性应变分布及形状对比
Figure 8. Equivalent plastic strain distribution and deformation of projectile after penetration
图 9 不同工况下弹体内能占总能量比值随时间的变化
Figure 9. Change of internal energy-to-total-energy ratio of the projectile with time in different cases
图 10 不同工况下弹与球形颗粒作用位置及距离
Figure 10. Interaction distance between projectile and aggregate in different cases
图 11 颗粒位置及强度变化时，弹体质心x向阻力及过质心z向力矩的时间历程（125 kHz低通滤波）
Figure 11. Time histories of x-directional resistant force and z-directional moment through projectile mass center for projectile with variation of location and strength of spherical aggregate (filtered by low pass filter with cutoff frequency 125 kHz)
图 12 参考工况下不同时刻弹体变形及弹靶相对位置
Figure 12. Projectile deformation and relative location of projectile and target at different times in the reference case
图 13 W-3工况下不同时刻弹体变形及弹靶相对位置
Figure 13. Projectile deformation and relative location of projectile and target at different times in Case W-3
图 14 颗粒尺寸变化时弹尖在xy平面内的运动轨迹
Figure 14. Trajectory of nose tip in xy plane with variation of aggregate diameter
图 15 颗粒尺寸变化时，弹体质心x向阻力及过质心z向力矩的时间历程（125 k Hz低通滤波）
Figure 15. Time histories of x-directional resistant force and z-directional moment through projectile mass center for the projectile with variation of aggregate diameter (filtered by low pass filter with cutoff frequency 125 k Hz)
表 1 半径为5倍弹径球体嵌埋位置及强度对弹体运动和变形的影响
Table 1. Movement and deformation of the projectile with the location and strength variation of the aggregate whose radius is 5 times of the projectile diameter
工况 速度/(m·s−1) 斜角/(°) 攻角/(°) 球形颗粒 |弹尖位移|max/mm 有效侵深/
mm最大转角/(°) 弹体变形 向下 向右 球心坐标/mm g1 x y z z 轴 y 轴 Ref. 1266 30 1.0 1.5 329 66 8 252 17.2 2.5 完整 W-1 1266 30 1.0 1.5 (50, 0, 0) 2 250 44 2 239 −21.2 −1.8 轻微弯曲 W-2 1266 30 1.0 1.5 (100, 0, 0) 2 266 53 13 204 17.4 2.5 完整 W-3 1266 30 1.0 1.5 (200, 0, 0) 2 239 140 27 163 84.2 59.6 弯曲 W-4 1266 30 1.0 1.5 (200, 25, 0) 2 263 50 8 203 16.2 2.5 完整 W-5 1266 30 1.0 1.5 (200, 50, 0) 2 277 33 12 223 11.6 2.7 轻微弯曲 W-6 1266 30 1.0 1.5 (200, 0, 0) 4 184 79 13 143 232.4 203.1 弯曲 注：(1)表中Ref.是Reference case的简称，表 2中Ref.与此内涵一致，不再赘述。
(2)观察方向沿弹体运动方向，从弹尾至弹尖。
(3)|弹尖位移|max表示弹尖位移最大值，表 2中|弹尖位移|max与此内涵一致。
(4)最大转角表示转角绝对值最大时的转角，正值表示逆时针方向转动，负值表示顺时针方向转动，表 2中内涵与此一致。
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表 2 球心(200,35,0)处球体半径对弹体运动的影响
Table 2. Movement of the projectile when spherical aggregates with different radii located at (200,35,0)
工况 速度/(m·s−1) 斜角/(°) 攻角/(°) 球形颗粒 |弹尖位移|max/mm 有效侵深/mm 绕z轴最大转角/(°) 向下 向右 半径/mm g1 x y Ref. 1 266 30 1.0 1.5 329 66 252 17.2 W-7 1 266 30 1.0 1.5 7.1 2 310 33 264 −24.1 W-8 1 266 30 1.0 1.5 14.2 2 295 34 251 −31.0 W-9 1 266 30 1.0 1.5 35.5 2 266 44 208 12.3 W-10 1 266 30 1.0 1.5 71.0 2 235 38 185 12.0
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