Theoretical Analysis on Shock Initiation of Performed Fragment to Uncovered Explosive
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摘要: 为了研究球形、圆柱形和正多棱柱形预制破片冲击起爆裸炸药的规律，利用Mathcad软件，基于Held高能炸药冲击起爆u2d判据进行了理论计算与分析，着重比较了破片的质量、密度、形状、长径比、棱数等对冲击起爆裸炸药特性的影响，并与AUTODYN的仿真结果进行了比较。结果表明：对于球形破片，直径一定时，破片密度增大, 质量增加，起爆能力增强；相同材料和直径的球形破片与长径比为1的圆柱形破片相比，圆柱形破片的起爆能力优于球形破片。对于圆柱形和正棱柱形破片，密度和质量一定时，随着长径比的增加，破片的起爆能力下降；正棱柱破片的棱数增加时，起爆能力降低，当棱数趋于无穷时，效果趋近于相应的圆柱形破片。Abstract: To research the laws of spherical, cylindrical, and regular prismatic preformed fragments initiating uncovered explosives, we adopted Mathcad software and the u2d criterion of Held to do the theoretical calculation and analysis.Influences of the preformed fragments' quality, density, shape, length to diameter ratio, and the number of edges were intercompared emphatically and were compared with the simulation results of AUTODYN.The results show that, for spherical fragments, when the diameter is certained, the initiating ability enhances as the density (or mass) of fragments increases; for spherical fragments and cylindrical fragments with a length to diameter ratio of 1, with the same material and diameter, the initiating ability of cylindrical fragments is better than that of spherical ones; for cylindrical and prismatic fragments of the same density and quality, as the length to diameter ratio increases, the fragments' initiating ability decreases; as the number of edges of regular prism fragment increases, the initiating ability decreases, when the edge number approaches infinite, its initiating ability converges with that of the corresponding cylindrical fragment.
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Key words:
- preformed fragments /
- fragment characters /
- uncovered explosive /
- initiation /
- critical criterion
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图 1 不同密度球形破片的临界速度与其质量m0的关系
Figure 1. The critical velocity of spherical fragment vs. m0 with different densities
图 2 不同形状破片临界速度与m0的关系
Figure 2. Critical velocity of fragment of different shapes vs. m0
图 3 正棱柱的正多边形截面等效为圆截面的过程
Figure 3. Process of the polygon cross section equivalent to circular cross section
图 4 圆柱形和正棱柱形破片临界速度随长径比的变化
Figure 4. Critical velocity of cylinder and regular prism fragments changing with the length to diameter ratio
图 5 正多棱柱破片的棱数对临界起爆速度的影响
Figure 5. Effect of the egde number n of regular prism fragment on the critical initiation velocity
表 1 3种不同类型破片的i值
Table 1. i value of 3 different types of fragment
Fragment shape i Sphere 6 Cylinder 4 Regular prism $\frac{2 \pi \cdot\left\{\sin \left[\left(1-\frac{2}{n}\right) \cdot \frac{\pi}{2}\right]+1\right\}^{2}}{n \cdot \sin \left[\left(1-\frac{2}{n}\right) \cdot \pi\right]}$ 
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