Non-Shock Ignition Probability of Octahydro-1,3,5,7-Tetranitro-Tetrazocine-Based Polymer Bonded Explosives Based on Microcrack Stochastic Distribution

We investigate stochastic microcracks of a heterogeneous microstructure as the primary mechanism determining the non-shock ignition probability of octahydro-1,3,5,7-tetranitro-1,2,3,5-tetrazocine-based polymer-bonded explosives. To quantify the ignition probability, we modify the viscoelastic cracking constitutive model by considering randomly distributed microcracks and combine this model with the hot-spot model and the Monte Carlo method. This method is validated by using a standard Steven test simulation, and we quantify how the microcrack stochasticity affects the ignition probability. The high-temperature region clearly changes compared with the case of single microcrack size. The discrepancy in the mechanical response of each element due to the heterogeneous microcracks causes a shear deformation, which increases the temperature. The difference between a uniform distribution and a normal distribution in microcrack size is also discussed. For a given impact velocity, the ignition probability for the normal microcrack size distribution exceeds that for the uniform microcrack size distribution. Although the two distributions have the same mean and variance, the real range in microcrack size corresponding to the normal distribution exceeds that for the uniform distribution. The results show that the sample radius does not significantly affect the ignition probability, whereas the opposite is true for the sample thickness. The ignition-probability curve is obtained in these cases. For sample dimensions of φ70 mm×13 mm, φ98 mm×13 mm, φ140 mm×13 mm, and φ98 mm×26 mm, the impact velocity thresholds corresponding to ignition probabilities in the range 0 %–99 % are 41.0–43.7, 41.0–44.3, 40.0–44.6, and 62.0–67.2 m/s, respectively, which is consistent with experimental results.