Numerical Analysis of Sensitivity of Tin Rayleigh-Taylor Instability to Model Parameters
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摘要: 利用自研的爆轰与冲击动力学欧拉计算程序和Steinberg-Guinan（SG）本构模型，数值模拟分析了样品初始参数（初始振幅、初始波长、样品初始厚度）和SG本构模型初始参数对爆轰驱动锡Rayleigh-Taylor（RT）不稳定性增长的影响。结果表明金属锡样品的初始参数对其RT不稳定性增长有很大的影响。RT不稳定性增长随着初始振幅的减小而减小，且存在一个截止初始振幅；存在一个最不稳定的模态（波长），当初始波长大于该波长时，RT不稳定性增长随着初始波长的减小而增大，反之，RT不稳定性增长随着初始波长的减小而减小；样品厚度的增大可以抑制RT不稳定性增长，而且存在一个样品截止厚度。金属锡的RT不稳定性增长对其SG本构模型应变硬化系数和应变硬化指数的变化不敏感，而对压力硬化系数和热软化系数比较敏感。从采用扰动增长法预估材料强度的角度来说，修正压力硬化系数以获得锡合理的材料强度是合理的途径。
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关键词:
- Rayleigh-Taylor不稳定性 /
- 材料强度 /
- 本构模型
Abstract: The sensitivity of Rayleigh-Taylor instability of tin driven by explosion to the initial parameters of sample (initial amplitude, wavelength and thickness of sample) and the initial parameters of SG constitutive model are numerical investigated by using an in-house Eulerian detonation and shock wave code. It concludes that the initial parameters of sample have a significant effect on the RT instability of Sn. The Sn RT instability grows more slowly with the initial amplitude decreasing, and a cutoff initial amplitude exists. A most unstable mode (wavelength) exists, when the initial wavelength is larger than this value, the RT instability grows faster as the initial wavelength diminishes; on the contrary, the RT instability grows slower as the initial wavelength decreases. The larger thickness of sample can restrain the growth of RT instability greatly, and a cutoff thickness of sample also exists. The Sn RT instability growth is not sensitive to the strain hardening coefficient and exponent, and it is greatly sensitive to the pressure hardening coefficient and thermal softening coefficient. But it should be a practical path to estimate the material strength of Sn through modifying the pressure hardening coefficient of SG model.-
Key words:
- Rayleigh-Taylor instability /
- material strength /
- constitutive model
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图 2 Lindquist等爆轰驱动铝实验的扰动振幅比较
Figure 2. Comparison of perturbation amplitudes of Lindquist et al.’s experiments driven by explosion
图 5 不同初始振幅时的扰动振幅增长曲线
Figure 5. Perturbation amplitude growth for different initial amplitude
图 6 不同初始波长时的扰动振幅增长曲线
Figure 6. Perturbation amplitude growth for different initial wavelength
图 7 不同样品初始厚度时的扰动振幅增长曲线
Figure 7. Perturbation amplitude growth for different initial thickness of sample
图 8 应变硬化系数不同时的扰动振幅增长曲线
Figure 8. Perturbation amplitude growth for different strain hardening coefficient
图 9 应变硬化指数不同时的扰动振幅增长曲线
Figure 9. Perturbation amplitude growth for different strain hardening exponent
图 10 压力硬化系数不同时的扰动振幅增长曲线
Figure 10. Perturbation amplitude growth for different pressure hardening coefficient
图 11 热软化系数不同时的扰动振幅增长曲线
Figure 11. Perturbation amplitude growth for different thermal softening coefficient
表 1 JO-9159炸药JWL状态方程参数
Table 1. EOS parameters of JO-9159 explosive
ρ0/(g·cm–3) pCJ/GPa DCJ/(km·s–1) α/GPa σ/GPa R1 R2 ω 1.86 36 8.862 934.8 12.7 4.6 1.1 0.37 
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表 2 锡的Mie-Grüneisen状态方程参数
Table 2. Mie-Grüneisen EOS parameters of Sn
ρ0/(g·cm–3) c/(km·s–1) γ0 $\alpha $ S1 S2 S3 7.287 2.61 2.18 0.47 1.51 0 0
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表 3 锡的SG本构模型参数
Table 3. SG constitutive model parameters of Sn
Y0/GPa Ymax/GPa G0/GPa β n A/GPa–1 B/K–1 0.16 0.22 17.9 2 000.0 0.06 0.086 6 2.12×10–3
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