Numerical simulation on spallation and fragmentation of tin under explosive loading
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摘要: 对爆轰加载下低熔点金属锡的层裂破碎问题开展了数值模拟。在利用实验数据对所采用数值方法和材料模型开展对比验证的基础上，通过对样品内部物理量时间及空间分布演化对比分析，剖析了冲击加-卸载中样品内部应力波与材料相互作用过程。此外，通过对比分析不同厚度锡样品在爆轰加载下的动态行为特征，进一步认识了自由面反射稀疏波、边侧稀疏波和入射稀疏波共同作用下层裂破碎演化机制。结果表明，当样品较薄时，层裂破碎行为由反射稀疏波主导；随着样品厚度的增大，反射稀疏波主导区缩小，入射稀疏波和边侧稀疏波主导区逐渐增大。Abstract: Spallation and fragmentation of tin, a low-melting point metal under explosive loading were numerically simulated. The numerical method and material model used were validated by the experimental results. Thereby, the temporal evolution and spatial distribution of the physical quantities in the Sn specimens were compared to explore the interaction between the stress waves and the material in the specimen under impact loading and unloading. Furthermore, the dynamic behaviors of the specimens with various thicknesses under explosive loading were in-depth analyzed to further understand the evolution mechanism of the spallation and fragmentation under the combination action of the reflective rarefaction wave from the free surface, the lateral rarefaction wave and the incident rarefaction wave. The results show that for the thin specimen, the early spallation and fragmentation are dominated by the reflective rarefaction wave. With increasing the thickness of the specimen, the region dominated by the reflective rarefaction wave becomes smaller, and meanwhile the region dominated by the incident rarefaction wave and the lateral rarefaction wave becomes larger.
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Key words:
- explosive loading /
- tin /
- spallation and fragmentation /
- stress wave /
- evolution mechanism
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图 2 冲击波到达自由表面时刻压力分布
Figure 2. Pressure distribution in the Sn specimen when the shock wave arriving at the free surface
图 3 样品中心轴线位置沿厚度方向的压力剖面演化
Figure 3. Evolution of pressure distribution along the central axis of the Sn specimen
图 4 锡样品中间点的压力和速度的演化
Figure 4. Evolutions of pressure and velocity at the centre of the Sn specimen
图 5 锡样品中心轴上不同厚度处的压力和速度的演化
Figure 5. Evolution of pressure and velocity at different sites along the central axis of the Sn specimen
图 8 起爆后6.4 μs时刻不同厚度Sn样品内部速度分布
Figure 8. Velocity distributions in the Sn specimens with different thicknesses at 6.4 μs after detonation
图 7 不同厚度锡样品中心轴上离底面0.5 mm处速度演化
Figure 7. The velocity evolution at x0=0.5 mm in the Sn specimens with different thicknesses
表 1 Sn和Al的SG本构参数
Table 1. The material parameters in SG constitutive relation for Sn and Al
材料 G0/GPa Y0/GPa Ymax/GPa $ \beta $ $ \eta $ $ {G_{{p}}'}$ $ {{{G}}_{{T}}'}/\rm{(MPa}\cdot {{\rm{K}}^{-1}}\rm{)}$ $ {Y_{{p}}'}$ $ {T_{{\rm{m0}}}}/{\rm{K}}$ Sn 17.9 0.16 0.22 2 000 0.06 1.55 −37.95 0.013 9 656.6 Al 2.86 0.26 0.76 310 0.185 1.86 −17.62 0.016 9 1 220 
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表 2 Sn和Al的Mie-Grüneisen状态方程参数
Table 2. The material parameters in Mie-Grüneisen equation of state for Sn and Al
材料 $ {{\rho }_{0}}\rm{/(g}\cdot \rm{c}{{\rm{m}}^{\rm{-3}}}\rm{)}$ $ {{c}_{0}}\rm{/(m}\cdot {{\rm{s}}^{-1}}\rm{)}$ $ {S_1}$ $ \gamma $ Sn 7.287 2 590 1.49 2.27 Al 2.785 5 328 1.338 2.0
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表 3 高能炸药JWL状态方程参数
Table 3. The parameters in JWL equation of state for high explosive
$ {{\rho }_{\rm{e}}}/(\rm{g}\cdot \rm{c}{{\rm{m}}^{-3}}\rm{)}$ $ D/\rm{(m}\cdot {{\rm{s}}^{-1}}\rm{)}$ $ {p_{\rm{e}}}/{\rm{GPa}}$ $ A/{\rm{GPa}}$ $ B/{\rm{GPa}}$ $ {R_1}$ $ {R_2}$ $ \omega $ $ {{e}_{\rm{e}}}\rm{/(GJ}\cdot {{\rm{m}}^{\rm{-3}}}\rm{)}$ 1.85 8 710 34.4 824.8 7.06 4.3 0.79 0.28 10.2
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