Coalescence Behavior of Voids during One-Dimensional Strain Spallation
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摘要: 延性金属的层裂行为包含孔洞成核、长大和聚集过程，其中孔洞聚集难以通过实验方法直接观测。采用有限元分析方法，研究了延性金属层裂过程中孔洞之间的聚集行为和竞争机制，讨论了孔洞间初始韧带距离、孔洞直径和孔洞位置分布对孔洞聚集的影响。通过实时统计孔洞长大过程中直径的变化，定量分析孔洞聚集的起始时刻。计算结果显示：当初始韧带距离由20 μm增加至50 μm时，相同孔径孔洞间聚集的起始时间不断延长，聚集时的直径增长加速度由1.717 Gm/s2降至0.602 Gm/s2；具有不同孔径比的孔洞之间发生聚集时，小孔优先向大孔靠拢；45°分布方式的孔洞在长大阶段的直径增长加速度最大，约为3.179 Gm/s2，且最早发生聚集。计算结果显示，在三孔聚集中，初始韧带距离和孔径相同的孔洞之间几乎同时发生聚集并贯通，且孔洞间聚集的起始时间随着初始韧带距离的增加而延长，大孔向附近小孔聚集的起始时刻较迟。计算结果揭示了层裂实验中难以观察到的孔洞长大和聚集的细观物理过程，对了解材料层裂的物理过程和本质具有重要的参考价值。Abstract: The spallation behavior of the ductile metals is a process involving nucleation, growth and coalescence of voids, and the coalescence of voids is difficult to directly observe experimentally. In this paper, the finite element analysis method was used to study the coalescence behavior and competition mechanism among the voids in the process of the ductile metal spallation. Influences of the initial ligament distance, the void diameter, and the void location distribution on the void coalescence were discussed. Through the real-time statistics of the change in diameter during the growth of the voids, the starting time of the coalescence of the voids was quantitatively analyzed. Results show that when the initial ligament distance increases from 20 μm to 50 μm, the initial time of coalescence among the same voids increases continuously, and the accelerations of the diameter increase decreases from about 1.717 Gm/s2 to 0.602 Gm/s2. When the coalescence occurs between voids with different aperture ratios, small voids preferentially aggregate to big voids. Voids with an angle of 45° have the largest diameter growth acceleration about 3.179 Gm/s2 in the growth stage, and the earliest coalescence occurs. For the coalescence among three voids, the calculation results show that the same voids with the same initial ligament distance aggregate and penetrate almost simultaneously, and the starting time of the coalescence between the voids increases with the increasing of the initial ligament distance. The aggregation of big voids to nearby small voids start later. Calculations in this paper reveal the mesoscopic physical process of void growth and coalescence, which is difficult to observe in spallation experiments, and have important reference value for the entire physical process and nature of the material spallation.
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Key words:
- ductile metals /
- spallation /
- voids coalescence /
- numerical simulation
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图 1 软回收靶板中孔洞的光学照片：(a) 相同孔洞，(b) 不同孔洞，(c) 3个孔洞，(d) 不同位置孔洞
Figure 1. Optical photo of voids in soft recycling target: (a) same voids, (b) different voids, (c) three voids, (d) voids in different position
图 3 点A和点B的位移时程曲线以及孔洞直径增长速率时程曲线
Figure 3. Time history curves of displacement of points A and B and void diameter growth rate
图 4 不同时刻下dIL0=20 μm的孔洞聚集演化云图
Figure 4. Evolution distribution of voids coalescence in dIL0=20 μm at different time
图 5 不同dIL0下孔洞直径增长速率时程曲线以及归一化聚集时间曲线
Figure 5. Time history curve of void diameter growth rate with different dIL0 and curve of normalized coalescence time
图 7 不同位置分布的孔洞直径增长速率时程曲线
Figure 7. Time history curves of voids diameter growth rate with different arrangement
图 8 不同时刻下不同位置分布的孔洞聚集演化云图
Figure 8. Evolution distribution of voids coalescence in different arrangement at different time
图 9 不同孔洞的直径增长速率时程曲线及孔洞横纵比曲线
Figure 9. Time history curves of different voids diameter growth rate and curves of voids horizontal to vertical ratio
图 10 不同时刻不同孔径比的孔洞聚集演化云图
Figure 10. Evolution distribution of voids coalescence in different aperture ratios at different time
图 11 不同ILD下各孔洞直径增长速率时程曲线
Figure 11. Time history curves of void diameter growth rate with different ILD
图 12 不同时刻不同初始韧带距离下三孔聚集演化云图
Figure 12. Evolution distribution of three voids coalescence in different ILD at different time
图 13 不同d3下孔洞直径增长速率时程曲线
Figure 13. Time history curves of void diameter growth rate with different d3
图 14 不同时刻不同d3条件下三孔聚集演化云图
Figure 14. Evolution distribution of three voids coalescence with different d3 at different time
表 1 高纯铜的Johnson-Cook本构、损伤及状态方程参数[20-21]
Table 1. Johnson-Cook constitutive, damage and equation of state parameters of high-purity copper[20-21]
ρ/(kg·m－3) A/MPa B/MPa C m n ${\dot \varepsilon}_0$/s–1 Troom/K Tmelt/K 8910 90 292 0.025 1.09 0.31 1 300 1356 C0/(m·s－1) s Γ0 G/GPa d1 d2 d3 d4 d5 3910 1.51 2 46.6 0.54 4.89 3.03 0.014 1.12 
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