A buring-crack network theoretical model for reaction evolution of explosives considering the inertial confinement effect of the shell motion
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摘要: 为合理描述机械约束下炸药装药点火后的反应演化行为，深入分析壳体变形运动特征，将壳体响应变化过程分为弹塑性准静态阶段、完全屈服运动阶段和壳体破裂后惯性运动约束阶段。考虑装药燃烧裂纹网络反应演化与壳体变形运动的耦合作用，建立了反映壳体运动惯性约束效应的装药反应演化模型，通过与典型实验结果进行对比，验证了模型及参数的适应性。壳体运动速度和内部压力的变化本质表征了装药能量释放与产物气体对外做功的关系，考虑壳体运动惯性约束效应可以更全面地表征装药反应演化过程，利用该模型，可以根据壳体壁面运动速度历史计算得到弹内压力、反应速率和反应度变化历史，可为约束装药在意外刺激下的安全性设计与评估提供理论支撑。
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关键词:
- 非冲击点火 /
- 反应演化行为 /
- 惯性约束效应 /
- 广义等效惯性约束刚度
Abstract: To reasonably describe the reaction evolution behavior of explosives after ignition under mechanical confinement, we conduct in-depth analysis of the deformation and movement characteristics of the shell, and divide the response process of the shell into three stages: elastoplastic stage, complete yield stage, and shell rupture stage with inertial motion constraint. The combustion rate theory and the combustion crack-network theory are employed as pivotal parameters for the reaction evolution of the explosives. In the initial stage, the mechanical properties of the shell are taken into consideration, with the material properties serving as the upper limit for structural constraint strength. During this stage, the deformation of the shell remains relatively small. In the second stage, a generalized equivalent stiffness concept is introduced in order to account for the inertial confinement effect of the shell movement. Furthermore, a mechanical deformation analysis of cylindrical shells and end caps is conducted, which takes into account the coupled effects of combustion crack network reaction evolution and shell deformation movement based on a kinematic theory. The third stage is building upon the foundation established in preceding stages, the impact of gas leakage following shell rupture on the progression of the explosive reaction process is considered, The integration of these three stages yields a formula for pressure, shell velocity, and time in the non-impact ignition reaction evolution process of solid explosives. A model for explosives reaction evolution is established to characterize the inertial confinement effects of the shell movement. This model and the related parameters are verified by comparing the calculating results with typical experimental data. It is found that the velocity of shell motion and the changes in internal pressure fundamentally characterize the relationship between the energy release of the explosives and the work done by the product gas. Considering the inertial confinement effects of shell motion is more indicative for the evolution process of explosives reaction, by using this model, the internal pressure of the shell, reaction rate and reaction degree of solid explosives can be calculated based on the historical changes in the velocity of the shell’s motion, thus providing a theoretical method for the explosive safety design and for evaluation under unexpected stimuli. -
图 1 约束装药燃烧裂纹扩展示意图
Figure 1. Schematic diagram of burning-crack propagation of confined explosives
图 2 端盖受均布压力和剪切力作用
Figure 2. End cover is subjected to uniform pressure and shear force
图 5 约束装药圆筒壁运动示意图
Figure 5. Schematic diagram of cylinder wall expansion motion of confined explosives
图 6 裂缝产物气体泄漏示意图（炸药应有燃烧裂纹）
Figure 6. Schematic diagram of leakage from product gas cracks
图 7 约束装药反应演化实验测试系统及装置
Figure 7. Experimental testing system and device for charge reaction evolution
图 8 （约束体厚度1 mm）装药反应演化过程压力和壳体运动速度变化历史的计算与实验结果的对比
Figure 8. Comparison between the calculating results and experimental data of the pressure profiles and wall velocity of the steel case with 1 mm wall thickness
图 9 （约束体厚度3 mm）装药反应演化过程压力和壳体运动速度变化历史的计算与实验结果的对比
Figure 9. Comparison between the calculating results and experimental data of the pressure profiles and wall velocity of the steel case with 3 mm wall thickness
图 10 （约束体厚度3和1 mm）约束装药反应度增长过程
Figure 10. Reaction growth of explosives under confinement with 3 and 1 mm wall thickness
图 11 （约束体厚度1 mm）惯性约束效应对装药反应演化过程压力和壳体运动速度的影响
Figure 11. Influence of the inertial effect on the calculated histories of the pressure profiles and wall velocity of the steel case with 1 mm wall thickness
图 12 （约束体厚度3 mm）惯性约束效应对装药反应演化过程压力和壳体运动速度变化历史的影响
Figure 12. Influence of the inertial effect on the calculated histories of the pressure profiles and wall velocity of the steel case with 3 mm wall thickness
图 13 装药尺寸对炸药装药点火后反应增长过程的影响
Figure 13. Influence of explosive size on the reaction growth after explosive charge ignition
图 14 壳体厚度对炸药装药点火后反应增长过程的影响
Figure 14. Influence of shell thickness on the reaction growth after explosive charge ignition
表 1 计算所需PBX8701炸药的热力学参数及壳体参数
Table 1. Thermodynamic parameters of PBX8701 and physical parameters of wall
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表 2 约束体厚度为1和3 mm时实验与理论模型壳体膨胀速度的对比
Table 2. Comparison between the experimental data and calculating results of wall velocity of the steel case with 1 and 3 mm wall thickness
约束体厚度/mm 壳体膨胀速度/(m·s−1) 误差/% 精度提高/% 实验峰值 模型峰值 无惯性 1 202.5/177.1 197.8 91.6 4.0 47.52 3 243.6 234.2 140.1 3.9 38.63
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