Molecular Dynamics Simulation of Micro-Jetting and Spallation in Helium-Bubble Copper under Double Supported Shocks
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摘要: 采用分子动力学方法，研究了含氦泡铜在两次稳态波加卸载作用下的微射流增长与损伤演化过程，对比了含氦泡与不含氦泡金属的损伤特征、激活应力阈值、微射流形态和速度分布以及不同区域氦泡的变形特征。结果表明：二次冲击后，氦泡膨胀的临界激活应力阈值低于孔洞形核的应力阈值，且与氦泡分布及氦泡数密度密切相关。低压首次冲击下，含氦泡金属比纯金属形成更显著的微射流；二次冲击下，氦泡使微射流更易断裂，且微射流头部最大速度更高，但微射流主体速度分布相当。二次冲击波对于已经经过首次冲击压缩、由于稀疏波作用发生轻微回弹但未恢复至初始状态的体氦泡几乎不起作用。二次冲击后，近表面已破裂飞出的氦泡壁也可能贴回气泡底部，使得部分氦原子被再次封存。二次冲击卸载后，被封存的氦泡会再次发生膨胀破裂，释放氦原子。在二次冲击作用下，氦泡塌缩机制与氦泡尺寸及冲击强度紧密关联。研究结果将为后续的辐照氦泡对金属微喷-微层裂耦合演化影响的跨尺度理论研究提供物理认识和理论依据。Abstract: Micro-jetting and micro-spallation at metal interfaces under intense shock loading play pivotal roles in applications such as inertial confinement fusion (ICF). These phenomena exhibit inherent complexity due to their multi-scale dynamics, strong nonlinearity, and coupled multi-field interactions. Under extreme irradiation conditions, the formation of high-pressure nanoscale helium bubbles significantly alters interface failure mechanisms. Using molecular dynamics methods, we investigate micro-jet growth and damage evolution in helium-containing copper subjected to double supported shock loadings. Helium bubbles demonstrate lower critical activation stress thresholds for expansion compared to void nucleation, with these thresholds being dependent on bubble distribution and number density. Under low-pressure primary shocks, helium-containing metals produce more pronounced micro-jets than pure metals. During secondary shocks, helium bubbles promote jet fragmentation, resulting in higher maximum velocities at micro-jet tips while maintaining comparable velocity distributions in micro-jet bodies. Secondary shocks show negligible effects on bulk helium bubbles that were previously compressed by initial shocks and partially rebounded due to rarefaction waves without complete recovery. Near-surface ruptured bubble walls may reattach to bubble bases after secondary shocks, temporarily re-trapping helium atoms that are subsequently released during unloading-induced re-expansion and rupture. The collapse mechanism of helium bubbles under secondary shock is closely related to the helium bubbles size and the strength of secondary shock. This study establishes fundamental physical understanding and provides a theoretical foundation for future cross-scale investigations of coupled micro-jetting and micro-spallation evolution in irradiated helium-containing metals.
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图 1 含氦泡金属铜的yz平面结构示意图（蓝色为铜基体，黄色为氦泡；冲击方向沿z轴；扰动自由表面另一侧的物质为真空）
Figure 1. Schematic diagram of the yz-plane microstructure of helium bubble-embedded copper (The copper matrix is depicted in blue, with helium bubbles represented by yellow regions. A shock wave is applied along the z-axis direction. The perturbed surface interfaces with a vacuum environment side.)
图 2 首次波后粒子速度为2.5、1.5、2.0 km/s的冲击加卸载下含氦泡铜和纯金属铜在不同时刻的动态破坏演化图像
Figure 2. Dynamic failure evolution images of copper with helium bubble and pure copper under shock loading and unloading with particle velocities of 2.5, 1.5 and 2.0 km/s after the first wave at different times
图 3 波后粒子速度为1.5 km/s时纯金属铜与含氦泡铜在不同时刻的应力波剖面曲线
Figure 3. Stress wave profile curves of pure copper and helium bubble-embedded copper at distinct time instants under a post-wave particle velocity of 1.5 km/s
图 4 up1为2.5 km/s、Δup2为1.0 km/s的冲击加卸载下纯铜与含氦泡铜在不同时刻的动态破坏演化图像，以及up1为1.5和2.0 km/s、Δup2为1.0 km/s的冲击加卸载下的界面破坏图像
Figure 4. Dynamic fracture evolution images of pure copper and helium bubble-embedded copper at distinct time instants under shock loading-unloading conditions with up1 of 2.5 km/s and a 1.0 km/s increment (after the second wave) and additional images for 1.5 and 2.0 km/s of up1 with the same 1.0 km/s increment (after the second wave)
图 5 up1为1.5 和2.0 km/s、Δup2为1.0 km/s的冲击加卸载工况下出现最大拉应力时刻的应力波剖面曲线
Figure 5. Stress wave profile curves at the moment of maximum tensile stress under loading-unloading conditions (up1 are 1.5 and 2.0 km/s with Δup2 of 1.0 km/s)
图 6 up1为1.5和2.0 km/s、Δup2为1.0 km/s的冲击加卸载情况下的微射流演化图像
Figure 6. Micro-jet evolution images under loading-unloading conditions (up1 are 1.5 and 2.0 km/s with Δup2 of 1.0 km/s)
图 7 up1为1.5 和2.0 km/s、Δup2=1.0 km/s的冲击加卸载下的速度-位置分布曲线
Figure 7. Velocity-position distribution curves （up1 are 1.5 and 2.0 km/s with Δup2 of 1.0 km/s）
图 8 含氦泡铜和纯铜微射流的径向分布函数
Figure 8. Radial distribution function for micro-jets in He bubble-containing copper and pure copper
图 9 初始构型中氦泡的分区与对应位置
Figure 9. Corresponding position of He bubbles in the initial configuration of Cu matrix
图 10 (a) up1=2.5 km/s、Δup2=1.0 km/s冲击加卸载下体氦泡1和体氦泡2的形态与特征尺寸变化以及(b)微射流底部氦泡6和6′在二次冲击作用下的形态演化
Figure 10. (a) Morphology and size changes of body helium bubbles 1 and 2; (b) morphological evolution of helium bubble 6 & 6′ at the micro-jet base under secondary impact (up1=2.5 km/s, Δup2=1.0 km/s)
图 11 up1=2.5 km/s、Δup2=1.0 km/s的二次冲击波传播过程中不同尺度氦泡的塌缩演化过程：(a) 速度着色，(b) 构造曲面网格方式显示，(c) 氦泡尺寸和二次冲击强度对氦泡塌缩机制影响相图
Figure 11. Collapse dynamics of helium bubbles across varying sizes during secondary shock wave propagation, with up1 of 2.5 km/s and Δup2 of 1.0 km/s: (a) colored in velocity, (b) displayed by constructing surface mesh, (c) phase diagram of the effect of helium bubble size and secondary shock strength on the collapse mechanism of helium bubbles
图 12 up1=2.0 km/s、Δup2=1.0 km/s的两次冲击加卸载过程中氦泡3 (a)、氦泡4 (b)、氦泡5 (c)、氦泡6/6′ (d)内压随时间变化
Figure 12. Pressure-time curves of helium bubble 3 (a), helium bubble 4 (b), helium bubble 5 (c), helium bubble 6/6′ (d) during shock loading and unloading (up1=2.0 km/s, Δup2=1.0 km/s)
图 13 不同加卸载路径下氦泡3在两次冲击后的压力(a)、温度(b)和体积(c)随时间的变化规律以及up1=2.0 km/s、Δup2=1.0 km/s时氦泡3的演化过程 (d)
Figure 13. Pressure (a), temperature (b), and volume (c) of helium bubble 3 evolved over time following two successive shocks under varying loading and unloading paths, and the evolution process of helium bubble 3 when up1=2.0 km/s and Δup2=1.0 km/s (d)
图 14 不同加卸载路径下氦泡4在两次冲击后的压力(a)、温度(b)和体积(c)随时间的变化规律以及up1=2.0 km/s、Δup2=1.0 km/s时氦泡4的演化过程 (d)
Figure 14. Pressure (a), temperature (b), and volume (c) of helium bubble 4 evolved over time following two successive shocks under varying loading and unloading paths, and the evolution process of helium bubble 4 when up1=2.0 km/s and Δup2=1.0 km/s (d)
图 15 不同加卸载路径下氦泡5在两次冲击后的压力(a)、温度(b)和体积(c)随时间变化规律以及up1=1.5 km/s、Δup2=1.0 km/s时氦泡5的演化过程 (d)
Figure 15. Pressure (a), temperature (b), and volume (c) of helium bubble 5 evolved over time following two successive shocks under varying loading and unloading paths, and the evolution process of helium bubble 5 when up1=1.5 km/s and Δup2=1.0 km/s (d)
图 16 不同加卸载路径下氦泡6和6′在两次冲击后的压力 (a)、温度 (b)和体积 (c)随时间的变化规律以及up1=2.0 km/s、Δup2=1.0 km/s时氦泡6和6′的演化过程 (d)
Figure 16. Pressure (a), temperature (b), and volume (c) of helium bubble 6 & 6′ evolved over time following two successive shocks under varying loading and unloading paths, and the evolution process of helium bubble 6 & 6′ when up1=2.0 km/s and Δup2=1.0 km/s (d)
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