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摘要: 为了实现对大尺寸材料试件的动态加载，得到与轻气炮加载应力波相同的爆炸加载冲击波，基于叠加原理，提出了利用炸药反向起爆模型完成对可压缩固体材料的冲击波加载。通过联立爆炸产物和可压缩流体的速度-压力曲线以及综合考虑炸药和材料试件各自由边所受稀疏波干扰的情况，从理论上给出了冲击波压力和冲击波加载平台宽度的计算方法。并结合数值模拟，对理论分析结果进行了验证，两者基本一致。Abstract: To achieve the dynamic loadings on the large -sized specimens by the explosive shock waves equivalent to the stress wave obtained by a light -gas gun, based on the principle of superposition, the reverse detonation model was introduced to accomplish the shock wave loading on the compressible solid materials.The interferences were comprehensively considered for each free edge of the explosives and the material specimens by the rarefaction waves.By integrating the velocity-pressure curves of the explosion products and the compressible fluids, the calculation methods were theoretically proposed for the shock pressure and the shock wave loading platform width, respectively.And the theoretical analysis results were verified by combining the numerical simulation.They are consistent with each other.
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Key words:
- mechanics of explosion /
- reverse detonation /
- shock wave /
- large -sized specimens /
- pressure /
- platform width
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图 1 三角形冲击波叠加成带平台的冲击波
Figure 1. Triangular waves superimposed into shock wave with platform
表 1 3种常用炸药和3种代表材料作用后的平台压力和粒子速度
Table 1. Shock wave platform pressure and particle velocity for three explosives loading three materials, respectively
炸药 ρ0/(t·m-3) DJ/(km·s-1) pJ/GPa cJ/(km·s-1) γ 固体 γ* ρ0*/(t·m-3) c0*/(km·s-1) u/(km·s-1) p/GPa TNT 1.630 6.93 19.570 5.198 3 Al 3 2.785 5.328 0.286 4.478 Cu 3 8.930 3.940 0.140 5.121 W 3 18.167 4.030 0.073 5.439 COMP B 1.717 7.98 27.335 5.985 3 Al 3 2.785 5.328 0.377 6.011 Cu 3 8.930 3.940 0.190 6.999 W 3 18.167 4.030 0.100 7.506 PETN1.77 1.770 8.30 30.484 6.225 3 Al 3 2.785 5.328 0.411 6.602 Cu 3 8.930 3.940 0.209 7.738 W 3 18.167 4.030 0.111 8.329 
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表 2 COMP B炸药反向起爆时，不同尺寸对应的理论平台宽度
Table 2. Theoretical platform width for several sizes in reverse detonation of COMP B
a1/mm a2/mm a3/mm t1/μs t2/μs t3/μs t4/μs te/μs 100 25 100 16.71 8.77 18.77 37.54 8.77 100 36 100 16.71 12.63 18.77 37.54 12.63 100 44 100 16.71 15.44 18.77 37.54 15.44 100 47 100 16.71 16.49 18.77 37.54 16.49 100 50 100 16.71 17.54 18.77 37.54 16.71 100 75 100 16.71 26.32 18.77 37.54 16.71 100 100 100 16.71 35.09 18.77 37.54 16.71 200 200 200 33.42 70.18 37.54 75.08 33.42 300 300 300 50.13 105.26 56.31 112.60 50.13 400 400 400 66.83 140.35 75.08 150.20 66.83
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表 3 平台压力和粒子速度的数值模拟结果
Table 3. Numerical simulation results of shock wave platform pressure and particle velocity
材料 理论计算 数值模拟 $\left( \frac{\left| \bar{p}-{{p}^{\prime }} \right|}{{{p}^{\prime }}}\times 100 \right)/%$ $\left( \frac{\left| \bar{u}-{{u}^{\prime }} \right|}{{{u}^{\prime }}}\times 100 \right)/%$ p/GPa u/(km·s-1) p/GPa u/(km·s-1) TNT + Al 4.478 0.286 4.320 0.272 3.66 5.15 TNT+Cu 5.121 0.140 4.967 0.134 3.10 4.48 TNT+W 5.439 0.073 4.555 0.062 19.41 17.74 COMP B+Al 6.011 0.377 5.870 0.362 2.40 4.14 COMP B+Cu 6.999 0.190 6.867 0.183 1.92 3.83 COMP B+W 7.506 0.100 6.828 0.089 9.93 12.36 PETN+Al 6.602 0.411 6.820 0.416 3.20 1.20 PETN+Cu 7.738 0.209 7.990 0.211 3.15 0.95 PETN+W 8.329 0.111 8.119 0.104 2.59 6.73
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表 4 冲击波平台宽度的数值模拟结果
Table 4. Numerical simulation results of shock wave platform width
序号 a1/mm a2/mm a3/mm te/μs t′e/μs $\left( \frac{\left| {{t}_{\text{e}}}-t_{\text{e}}^{\prime } \right|}{t_{\text{e}}^{\prime }}\times 100 \right)/%$ 1 100 25 100 8.77 8.12 8.03 2 100 36 100 12.63 12.20 3.54 3 100 44 100 15.44 15.06 2.51 4 100 47 100 16.49 16.12 2.30 5 100 50 100 16.71 16.40 1.88 6 100 75 100 16.71 16.45 1.57 7 100 100 100 16.71 16.56 0.90 8 200 200 200 33.42 33.83 1.22 9 300 300 300 50.13 50.26 0.27 10 400 400 400 66.83 67.05 0.32
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