Effect of Projectile Geometry on Dynamic Mechanical Response of Graphene
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摘要: 为探究弹丸几何形状对石墨烯动态力学响应的影响，考虑了不同形状以及同种形状下不同结构尺寸比例的两种弹丸设计方案，借助分子动力学模拟进行计算，通过表征弹丸的剩余速度、动能损耗以及石墨烯自身破坏的状况和应力波的传播状态研究石墨烯受到冲击时的响应。结果表明：不同形状弹丸冲击石墨烯的剩余速度和动能消耗随冲击速度的变化大致可分为3个区域，其中球形和半球形弹丸冲击情况类似，柱形弹丸的差异性较大；柱形弹丸对石墨烯的破坏要强于球形和半球形弹丸，分形理论模型能够较好地量化描述石墨烯破孔样貌；柱形弹丸自身平头部产生的“屏障效应”能够较好地解释其侵彻单层和双层石墨烯的弹道极限速度分别小于和接近球形和半球形冲击时的弹道极限速度；同种形状下，弹丸结构尺寸比例增大，弹丸侵彻能力增强，但尺寸比增大所带来的优势不具有持续增强性。Abstract: In order to explore the influence of projectile geometry on the dynamic mechanical response of graphene, two projectile designs with different shapes and different structural size ratios under the same shape have been considered using molecular dynamics simulation. The mechanical response of single/multi-layer graphene under impact was studied by characterizing the residual velocity of the projectile, kinetic energy consumption, the damage state of graphene and the propagation state of stress wave. The results show that the residual velocity and kinetic energy consumption of different shapes of projectiles impacting graphene can be roughly divided into three regions with the change of impact velocity. The impact of spherical and hemispherical projectiles is similar, but cylindrical projectiles exhibits large difference. The damage of graphene by cylindrical projectiles is stronger than those by spherical and hemispherical projectiles, and the fractal theory model can quantitatively describe the morphology of graphene holes. The “barrier effect” generated by the flat head of cylindrical projectiles can better explain the ballistic limit velocities of penetrating monolayer and bilayer graphene, which are lower than or close to those of spherical and hemispherical impact, respectively. For the same shape of hemispherical projectile, the penetration capability increases with the increase of the size ratio, but the enhancing effect brought about by the increase of the size ratio does not last continuously.
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图 1 球形、半球形和柱形弹丸示意图
Figure 1. Schematic diagram of spherical, hemispherical and cylindrical projectiles
图 2 5种不同结构尺寸比例（L/R）的半球形弹丸示意图
Figure 2. Schematic diagram of five kinds hemispherical projectiles with different length-radius ratios (L/R)
图 3 冲击模型示意图（红色部分为冲击区域，黄色部分为固定区域，蓝色部分为球形弹丸）
Figure 3. Schematic diagram of impact model (The red part is the impact area, the yellow part is the fixed area and the blue part is the spherical projectile.)
图 4 弹丸的剩余速度与动能损耗随初始速度的变化趋势
Figure 4. Variations of residual velocity and kinetic energy consumption of projectiles with initial velocity
图 5 在6.0 km/s冲击速度下双层石墨烯碳原子的速度分布
Figure 5. Velocity distribution of double-layer graphene carbon particles under the impact velocity of 6.0 km/s
图 6 不同形状弹丸以不同速度冲击时脱离时刻双层石墨烯z向位置云图
Figure 6. Contour plots of z-direction position of double-layer graphene impacted by different shapes of projectiles with different velocities at the time of separation
图 7 不同形状弹丸冲击下破孔参数A和S11随初始速度的变化
Figure 7. Morphological parameters A and S11 of the hole as a function of initial impact velocity ranging under the impact of different shapes of projectiles
图 8 3种不同形状弹丸冲击不同层数（1～4层）石墨烯的剩余速度随初始速度的变化
Figure 8. Variations of residual velocity with initial velocity of three shape projectiles impacting different layers (1–4 layers) of graphene
图 9 不同形状弹丸冲击双层石墨烯时弹丸受力随时间的变化
Figure 9. Change of force with time on projectile impacting double-layer graphene
图 10 柱形与半球形弹丸以3.5 km/s冲击双层石墨烯时破坏时刻的样貌侧视图和仰视图
Figure 10. Side view and bottom view of cylindrical and hemispherical projectiles impacting double-layer graphene at 3.5 km/s
图 11 不同时刻柱形弹丸冲击石墨烯的z向位置云图
Figure 11. z-direction position contour plots of graphene under the impact of cylindrical projectile at different times
图 12 柱形弹丸冲击下不同时刻石墨烯中剪切应力分布云图
Figure 12. Distribution of shear stress in graphene at different times under cylindrical projectile impact
图 13 不同尺寸比例半球形弹丸冲击双层石墨烯时剩余速度和动能损耗随冲击速度的变化
Figure 13. Variations of residual velocity and kinetic energy consumption with initial velocity ofdifferent length-radius ratios projectiles impacting double-layer graphene
图 14 不同L/R的弹丸冲击10层石墨烯的侵彻深度随初速度的变化
Figure 14. Variations of penetration depth of ten-layer graphene with initial impact velocity of different length-radius ratios projectiles
表 1 不同形状弹丸冲击不同层数石墨烯的弹道极限速度
Table 1. Ballistic limit velocities of different shape projectiles impacting different layers of graphene
Shape of projectile vbl/(m·s−1) Single-layer Double-layer Triple-layer Quadruple-layer Spherical 3360 3890 4230 4470 Hemispherical 3330 3740 4180 4450 Cylindrical 2950 3860 4660 5250 
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