Phase Field Modeling of the Evolution of Helium Bubbles in Shock Loaded Aluminum
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摘要: 氦泡等缺陷对金属材料动态强度的影响一直是动态强度研究关注的重点。将相场方法引入冲击加载下氦泡演化行为研究中，通过与晶体塑性理论耦合，建立了可描述冲击下氦泡早期演化行为的介观模拟技术。应用该方法，针对含氦泡的金属铝材料，从介观尺度对氦泡的演化行为及其对位错集体演化行为的影响进行了研究。结果表明：氦泡结构的非均匀性导致局域应力集中和塑性变形集中，局域塑性变形集中会导致沿冲击波传播方向发射稀疏波；从能量守恒角度上看，在材料变形过程中氦泡生长与塑性变形呈竞争关系，塑性耗散的快慢直接影响氦泡的生长速率，使其发生改变。研究结果可为解读含氦泡材料的宏观屈服强度和层裂行为提供理论支撑。Abstract: Investigation of the influence of helium bubbles on the dynamic strength has drawn continuous attention. In this article, the phase field method (PFM) is applied to investigate the evolution of helium bubbles at an early stage in shock-loaded aluminum based on its advantage to describe the interface evolution. PFM is coupled with the crystal plasticity finite element method (CPFEM), which makes it possible to investigate the interaction between the helium bubbles and the collective behaviors of dislocation assembles. It is found that the heterogeneity of helium bubbles induces a local concentration of plastic deformation, which leads to a rarefaction wave along the propagation direction of the shock wave. From an energy perspective, it is inferred that both the growth of helium bubbles and the plastic deformation are driven by the strain energy, which indicates that these two processes may compete with each other.
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Key words:
- shock loading /
- helium bubble /
- phase field method /
- crystal plasticity
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图 3 冲击波到达后（0.1 ns时刻）氦泡附近的局域化效应
Figure 3. Localization effect near the helium bubble at the arrival of the shock wave (0.1 ns)
图 4 冲击压缩过程中可动位错密度的演化
Figure 4. Evolution of mobile dislocation density during shock compression
图 5 不同时刻氦泡周围的可动位错密度分布
Figure 5. Distribution of the mobile dislocation density around helium bubbles at different time
图 6 不同时刻氦泡序参量的空间分布
Figure 6. Spatial distribution of order parameter at different times
图 7 第1次与第2次卸载波到达后氦泡的演化行为
Figure 7. Evolution of helium bubbles when the first and second unloading waves arrive
图 9 氦泡附近纵向应力演化历史
Figure 9. Time history of longitudinal shear stress near the helium bubbles
图 10 在300 K环境温度、100 m/s的加载速度下不同模型模拟的氦泡长大速率
Figure 10. Growth rates of helium bubbles simulated by different constitutive models at 300 K and impact velocity of 100 m/s
图 11 不同环境温度下氦泡生长速率对比
Figure 11. Comparison of growth rates of helium bubble at different ambient temperatures
图 12 不同初始位错密度下氦泡生长速率的对比
Figure 12. Comparison of growth rates of helium bubble under different initial dislocation densities
图 14 1.0 ns时刻氦泡附近的可动位错密度与临界分切应力分布
Figure 14. Contours of mobile dislocation density and critical shear stress near helium bubble at 1.0 ns
图 15 两个氦泡距离较远时1.0 ns时刻的序参量分布
Figure 15. Distribution of order parameters at 1.0 ns when two helium bubbles are far apart
图 16 较多初始氦泡时的冲击演化行为
Figure 16. Impact evolution behavior of more initial helium bubbles
表 1 状态方程参数与声子拖曳系数
Table 1. Parameters of equation of states and phonon drag coefficients
Material ${\,\rho }{_{0} }/$(g·cm−3) ${c}{_{0}}/$(m·s−1) $ \lambda $ $\varGamma$ ${B}{_{0}}/$(10−5 Pa·s) ${B{'} }{_{T} }$/(10−7 Pa·s·K−1) Al 2.77 5320 1.38 2.10 1.34 1.00 
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表 2 弹性常数及其关于温度的导数
Table 2. Elastic constants and temperature derivatives of the elastic constants
Material ${c}{_{11}}$/GPa ${c}{_{12}}$/GPa ${c}{_{44}}$/GPa $\dfrac{ \mathrm{d}{c}{_{11} } }{\mathrm{d}T } \big/$(GPa·K−1) $\dfrac {\mathrm{d}{c}{_{12} } }{\mathrm{d}T} \big/$(GPa·K−1) $\dfrac {\mathrm{d}{c}{_{44} } }{\mathrm{d}T } \big/$(GPa·K−1) Al 114.22 61.94 31.60 −3.83 −0.68 −1.51
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表 3 晶体塑性模型参数
Table 3. Parameters of the crystal plasticity model
Material ${\alpha }{_{\mathrm{H}\mathrm{N} }}$/m−2 ${\alpha }{_{\mathrm{M}\mathrm{u}\mathrm{l}\mathrm{t} } }$ ${\alpha }{_{\mathrm{a}\mathrm{n}\mathrm{n}\mathrm{i} } }$ ${v}{_{\mathrm{I} }}$/(m·s−1) ${A}{_{\mathrm{I} } }$ ${\tau }{_{0}}$/MPa ${\,\rho }{_{\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l} } }$/m−2 Al 1.0×1022 0.51 10 1.0 0.4 22 1×1011
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表 4 相场模型参数
Table 4. Parameters of the phase field model
Materail $ L/ $(${\mathrm{P}\mathrm{a} }{^{-1} }{\cdot \mathrm{s} }{^{-1} }$) $\,\beta$/N $W/\left(\mathrm{J}{\cdot \mathrm{k}\mathrm{g} }{^{-1} }{\cdot \mathrm{K} }{^{-1} }\right)$ Al 500 0 0
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