Application of SPH Method for Problem of Rock Penetration within the Wide-Ranged Velocity
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摘要: 采用光滑粒子流体动力学（SPH）方法对花岗岩靶板受碰撞侵彻的大应变、高应变率变形问题进行了数值模拟。为了描述弹目材料的非线性变形及破坏特性，对花岗岩靶板引入了Holmquist-Johnson-Cook（HJC）本构模型及损伤模型，对弹体引入含损伤的Johnson-Cook（J-C）本构方程和Grüneisen状态方程，靶板与弹体均离散成拉格朗日粒子。通过自编程序仿真计算0～4 m/s的着靶速度下花岗岩靶板的三维侵彻过程，对比分析了钢珠在不同弹体条件下的侵彻结果，在固体侵彻、半流体侵彻和流体侵彻的区域内拟合了侵彻深度随着靶速度的变化曲线。数值计算结果显示，侵彻深度随着靶速度的增加在固体侵彻区间（
$ {v_0} <1421\;{\rm{m}}/{\rm{s}}$ ）呈现递增趋势，在半流体侵彻区间（$ 1421\; {\rm{m}}/{\rm{s}} \leqslant {v_0}\leqslant1700 \;{\rm{m}}/{\rm{s}}$ ）呈现递减趋势，在流体侵彻区间（${v_0} > 1700\;{\rm{m}}/{\rm{s}} $ ）呈现递增趋势并逐渐趋于平滑，达到峰值。-
关键词:
- 弹体 /
- 侵彻 /
- 花岗岩 /
- 光滑粒子流体动力学方法
Abstract: The smoothed particle hydrodynamics (SPH) method is used to simulate the deformation of penetration of granite at large strain and high strain rates. In order to describe the nonlinear deformation and failure characteristics of the projectile and target, the Holmquist-Johnson-Cook (HJC) constitutive model, damage model, Johnson-Cook (J-C) constitutive model and Grüneisen equation of state for granite are introduced, in which the projectile and the fortifications are discretized into Lagrangian particles. In simulation of three-dimensional penetration process of granite targets by self-made program at the speed from 0 m/s to 4000 m/s, we compare and analyzes the penetration results of steel balls under different projectile conditions. The curve of the penetration depth with the penetration velocity is fitted in solid penetration, semi-fluid penetration and fluid invasion. The numerical results show that the penetration depth increases with the increase of the penetration velocity in the solid penetration interval ($ {v_0} < 1421\;\,{\rm{m}}/{\rm{s}} $ ). A decreasing trend is shown in the semi-fluid penetration interval ($ 1421\;{\rm{m}}/{\rm{s}} \leqslant {v_0} \leqslant 1700\;{\rm{m}}/{\rm{s}} $ ), while an increasing trend is shown in the fluid penetration interval ($ 1421\;{\rm{m}}/{\rm{s}} < {v_0} <1700\;{\rm{m}}/{\rm{s}} $ ) and gradually tended to reach the peak.-
Key words:
- projectile /
- penetration /
- granite /
- smoothed particle hydrodynamics method
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图 3 不同速度下SPH数值模拟的成坑结果
Figure 3. Results of the pit at diferent penetration velocities by SPH
图 10 0～4000 m/s速度范围内弹体分段作为刚体和非刚体的侵彻深度随着靶速度的变化
Figure 10. Value of the penetration depth and the penetration velocity from 0 to 4000 m/s
图 11 0～800 m/s的初速度范围内刚体弹和非刚体弹体的侵彻深度随着靶速度的变化
Figure 11. Penetration depth vs. penetration velocity from 0 to 800 m/s
图 12 0～4000 m/s的初速度范围内非刚体弹侵彻深度随着靶速度的变化关系
Figure 12. Penetration depth vs. penetration velocity from 0 to 4000 m/s
图 13 1000～1600 m/s的着靶速度范围内非刚体弹侵彻深度随着靶速度的变化
Figure 13. Penetration depth vs. penetration velocity from 1000 to 1600 m/s
表 1 花岗岩靶板的HJC强度模型参数
Table 1. Strength model parameters for the granite
G/GPa ρ/(kg∙m−3) A/MPa B/MPa N ${\dot \varepsilon _0}/{s^{ - 1}}$ C fc′/MPa Smax D1 D2 εf 14.19 2800 950 1600 0.79 1.0 0.008 126.5 70 0.034 1.0 0.01 
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表 2 花岗岩靶板的HJC状态方程参数
Table 2. Equation of state parameters for the granite
pc/MPa μc pl/MPa μl T/MPa K1/GPa K2/GPa K3/GPa 42.2 0.003 279 0.02 8.786 85 –171 208
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表 3 钢珠的材料参数
Table 3. Strength model parameters for the projectile
G/GPa ρ/(kg∙m−3) σy/GPa B/GPa N C1/(m∙s−1) C Tmelt/K S1 γ0 M 81.8 7800 0.235 0.3 1.03 3574 0.26 1600 1.92 1.69 0.014
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表 4 SPH数值模拟的侵彻深度结果
Table 4. Depth of pit formed by numerical simulation of SPH
v0/(m∙s−1) h/mm v0/(m∙s−1) h/mm 97 3.01 202 4.20 109 3.29 251 4.72 171 3.96 269 4.91 175 3.97
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