Abstract
In order to well predict mean explosive particle size effects on the shock-to-detonation transition (SDT) process of a plastic bonded explosive (PBX), some improvements to a previous three-term mesoscopic reaction rate model that consists of a hot-spot ignition term, a hot-spot growth term, and an overall reaction term are made: A set of new switch conditions, which depend on mean explosive particle size, is proposed for the operations of the three terms; a new expression is obtained for the hot-spot growth term by combining an ignition efficiency factor which depends on mean explosive particle size and replacing the original burning topology geometric factor, which merely describes the characteristic of the outward pore surface burning reaction, by a more reasonable one, which combines the characteristic of inward particle surface burning reaction and that of outward pore surface burning reaction. Furthermore, for verification, the improved reaction rate model is incorporated into the DYNA2D code to simulate numerically the SDT process of three formulations of PBXC03 having the same density but different mean particle sizes, and the numerical results of pressure histories at different Lagrangian locations in the explosive are found to be in good agreement with previous experimental data.
Similar content being viewed by others
References
Forest, C.A.: Burning and Detonation. Los Alamos Scientific Laboratory Report LA-UR-81-839 (1981). https://www.osti.gov/biblio/6586749/
Tarver, C.M.: Ignition and growth modeling of LX-17 hockey puck experiments. Propellants Explos. Pyrotech. 30(2), 109–117 (2010). https://doi.org/10.1002/prep.200400092
Tang, P.K., Johnson, J.N., Forest, C.A.: Modeling heterogeneous high explosive burn with an explicit hot-spot process. Proceedings of the 8th Symposium (International) on Detonation, Albuquerque, NM, pp. 52–61 (1985)
Kaneswaran, M.A., Curtis, J.P., Reaugh, J.E.: Modeling the shock to detonation transition in PETN using CREST. Proceedings of the 15th International Detonation Symposium, San Francisco, CA, pp. 1042–1051 (2014)
Starkenberg, J.: Shock-pressure and pseudo-entropic approaches to explosive initiation modeling. Proceedings of the 15th International Detonation Symposium, San Francisco, CA, pp. 908–916 (2014)
Wescott, B.L., Stewart, D.S., Davis, W.C.: Equation of state and reaction rate for condensed-phase explosives. J. Appl. Phys. 98(5), 053514 (2005). https://doi.org/10.1063/1.2035310
Massoni, J., Saurel, R., Baudin, G., Demol, G.: A mechanistic model for shock initiation of solid explosives. Phys. Fluids 11(3), 710–736 (1999). https://doi.org/10.1063/1.869941
Hamate, Y., Horie, Y.: Ignition and detonation of solid explosives: a micromechanical burn model. Shock Waves 16(2), 125–147 (2006). https://doi.org/10.1007/s00193-006-0038-x
Kim, K., Sohn, C.H.: Modeling of reaction buildup processes in shock porous explosive. Proceedings of the 8th Symposium (International) on Detonation, Albuquerque, NM, pp. 926–933 (1985)
Kim, K.: Development of a model of reaction rates in shocked multicomponent explosives. Proceedings of the 9th Symposium (International) on Detonation, Portland, OR, pp. 593–603 (1989)
Duan, Z.P., Wen, L.J., Liu, Y., Ou, Z.C., Huang, F.L.: A pore collapse model for hot-spot ignition in shocked multi-component explosive. Int. J. Nonlinear Sci. Numer. Simul. 11(Supplement), 19–24 (2011). https://doi.org/10.1515/IJNSNS.2010.11.S1.19
Zhang, Z.Y., Lu, F.Y., Wang, Z.B., Huan, S.: Studies on high-pressure reaction rate of PBX-9404. Explos. Shock Waves 19(4), 360–364 (1999) (in Chinese)
Wen, L.J.: Research on mesoscopic reaction rate model of shock initiation of PBX. Ph.D. Thesis, Beijing Institute of Technology (2011) (in Chinese)
Duan, Z.P., Liu, Y.R., Zhang, Z.Y., Ou, Z.C., Huang, F.L.: Prediction of initial temperature effects on shock initiation of solid explosives by using mesoscopic reaction rate model. Int. J. Nonlinear Sci. Numer. Simul. 15(5), 299–305 (2014). https://doi.org/10.1515/ijnsns-2013-0056
Liu, Y.R., Duan, Z.P., Zhang, Z.Y., Ou, Z.C., Huang, F.L.: A mesoscopic reaction rate model for shock initiation of multi-component PBX explosives. J. Hazard. Mater. 317, 44–51 (2016). https://doi.org/10.1016/j.jhazmat.2016.05.052
Wen, L.J., Duan, Z.P., Zhang, L.S., Zhang, Z.Y., Ou, Z.C., Huang, F.L.: Effects of HMX particle size on the shock initiation of PBXC03 explosive. Int. J. Nonlinear Sci. Numer. Simul. 13(2), 189–194 (2012). https://doi.org/10.1515/ijnsns-2011-129
Moulard, H.: Particular aspect of the explosive particle size effect on shock sensitivity of cast PBX formulations. Proceedings of the 9th Symposium (International) on Detonation, Portland, OR, pp. 18–24 (1989)
Price, D.: Effect of particle size on the shock sensitivity of porous HE. J. Energ. Mater. 6(3–4), 283–317 (1988). https://doi.org/10.1080/07370658808012557
Zhang, J., Jackson, T.L.: Effect of microstructure on the detonation initiation in energetic materials. Shock Waves (2017). https://doi.org/10.1007/s00193-017-0796-7
Sutherland, G.T., Zakraysek, A.J.: Modeling of the effect of crystal quality and particle size on the shock reactivity and detonation properties of simple nitramine based explosives. Proceedings of the 13th Symposium (International) on Detonation, Norfolk, VA, pp. 23–28 (2006)
Garcia, F., Vandersall, K.S., Tarver, C.M.: Shock initiation experiments with ignition and growth modeling on low density HMX. J. Phys. Conf. Ser. 500(5), 052048 (2014). https://doi.org/10.1088/1742-6596/500/5/052048
Howe, P., Frey, R., Taylor, B., Boyle, V.: Shock initiation and the critical energy concept. Proceedings of the 6th Symposium (International) on Detonation, Arlington VA, pp. 11–19 (1976)
Tarver, C.M., Chidester, S.K., Nichols, A.L.: Critical conditions for impact- and shock-induced hot spots in solid explosives. J. Phys. Chem. 100(14), 5794–5799 (1996). https://doi.org/10.1021/jp953123s
Taylor, B.C., Ervin, L.W.: Separation of ignition and buildup to detonation in pressed TNT. Proceedings of the 6th Symposium (International) on Detonation, Arlington VA, pp. 3–10 (1976)
Khasainov, B.A., Ermolaev, B.S., Presles, H.N., Vidal, P.: On the effect of grain size on shock sensitivity of heterogeneous high explosives. Shock Waves 7(2), 89–105 (1997). https://doi.org/10.1007/s001930050066
Carroll, M.M., Holt, A.C.: Static and dynamic pore-collapse relations for ductile porous materials. J. Appl. Phys. 43(4), 1626–1636 (1972). https://doi.org/10.1063/1.1661372
Greenaway, M.W., Gifford, M.J., Proud, W.G., Field, J.E., Goveas, S.G.: An investigation into the initiation of hexanitrostilbene by laser-driven flyer plates. AIP Conf. Proc. 620, 1035–1038 (2002). https://doi.org/10.1063/1.1483715
Starkenberg, J.: Modeling detonation propagation and failure using explosive initiation models in a conventional hydrocodes. Proceedings of 12th Symposium (International) on Detonation, San Diego, CA (2002)
Hussain, T., Liu, Y., Huang, F., Duan, Z.P.: Ignition and growth modeling of shock initiation of different particle size formulations of PBXC03 explosive. J. Energ. Mater. 34(1), 38–48 (2016). https://doi.org/10.1080/07370652.2014.995324
Acknowledgements
The authors gratefully acknowledge the financial support for the present study by the National Natural Science Foundation of China under Grant U1630113. The authors also thank the anonymous reviewers for their careful work and thoughtful suggestions that have helped improve this paper substantially. Finally, the authors would like to thank the Managing Editor and Xia Jin for their linguistic assistance during the preparation of this manuscript.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by A. Higgins.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Liu, Y.R., Hu, X.M., Duan, Z.P. et al. A mesoscopic reaction rate model for shock-to-detonation of PBX explosives having different mean particle sizes. Shock Waves 29, 559–571 (2019). https://doi.org/10.1007/s00193-018-0875-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00193-018-0875-4