A theoretical model of PBXs’ tensile strength based on meso-structure parameters
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摘要: 为给塑性黏结炸药（PBX）的力学强度设计提供支撑、探索材料细观特征量与材料强度之间的定量规律，应用微裂纹扩展区理论，将PBX炸药的单轴拉伸过程中力学响应特征的变化归结为扩展裂纹取向角度的增加，将扩展裂纹最大取向角与拉伸强度相关联，构建了基于材料细观特征量的拉伸强度理论模型，并采用不同温度的单轴拉伸实验验证了该理论模型的有效性。研究表明：该拉伸强度理论模型可以实现对PBX炸药拉伸强度与炸药微裂纹密度、颗粒/黏结剂界面性能以及颗粒/黏结剂体系的表观杨氏模量、泊松比等细观特征量之间关系的定量描述。Abstract: In practical applications, plastic bonded explosive (PBX) explosives are often used as load bearing structural components. Hence, the mechanical strength is an important parameter in PBXs’ design. It is of great interest how to adjust the microscopic characteristics of the material in the manufacturing process to obtain an PBX with the required strength. PBX consists of a large portion of energetic particles with a small portion of binder. Therefore, a large number of randomly distributed microcracks exist inside. Inspired by the successful application of microcrack extension mechanism in the PBXs’ mechanical response simulation in recent years, the theory related to microcrack extension was applied to the strength modeling study. The domain of microcrack growth (DMG) theory was applied to analyze PBXs’ uniaxial tension. The results shows that the increase in tensile load resulted in microcrack extension at different orientation angles, as well as a decrease in the crack interval. Meanwhile, recent studies on the cascading behavior of randomly distributed microcracks show that the crack cascading behavior with each other is controlled by the orientation angle and crack interval of adjacent cracks. The PBX tensile fracture comes from the instable extension of macroscopic cracks, and the macroscopic crack formation and extension both come from the cascading of microcracks. By treating the strength as the minimum load required for catastrophic crack cascade extension, there is a one-to-one correspondence between the strength and the maximum orientation angle of extended crack. Based on the DMG theory, this one-to-one correspondence is expressed as the theoretical model of tensile strength. This theoretical model establishes the connection between the tensile strength and the meso-structure parameters such as stress intensity factor, microcrack diameter and microcrack density. Comparison of tensile strength model predictions with wide temperature range (from –40 ℃ to 45 ℃) experimental data, indicated that this model is capable to describe the PBXs’ tensile strength. Suggestions for the design of strength enhancement of PBXs can be provided by this theoretical model.
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Key words:
- PBX /
- tensile strength /
- theoretical model /
- meso damage /
- DMG theory
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图 5 两种应力强度因子（KⅠC和KⅡC）对材料强度的影响
Figure 5. Curves of tensile strength with two stress intensity factors (KⅠC and KⅡC)
表 1 与温度无关的PBX-3细观特征量
Table 1. Temperature independent mesoscopic characteristics of PBX-3
n/cm−3 a0/cm au/cm v 1372 0.006352 0.03703 0.3 
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表 2 与温度相关的PBX-3细观特征量
Table 2. Temperature dependent mesoscopic characteristics of PBX-3
T/℃ KⅠC/（MPa·cm1/2） KⅡC/（MPa·cm1/2） −40 0.1628 0.1911 −30 0.1502 0.1763 −25 0.1556 0.1827 −20 0.1520 0.1784 −10 0.1457 0.1711 25 0.1457 0.1711 45 0.1322 0.1552
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