Modeling of Shock Loading Processes in Heterogeneous Materials Based on Boron Carbide with the Addition of Chromium Diboride (Crb_2)

The results of a comprehensive experimental-computational study of the dynamic behavior of B_4C-CrB_2 composite materials in the loading-velocity range up to 1650 m/s are presented. To describe the response of chromium diboride (CrB_2), an approach based on an additive mixture model is proposed, which made it possible, by interpolating available experimental data, to construct the material's shock adiabat (Hugoniot) in the velocity range up to 2000 m/s. The model was validated by comparing the results of numerical simulations of high-velocity impact with experimental data. The criteria for agreement were the crater geometry and the morphology of the fracture surface.

Keywords

chromium diboride CrB2; shock adiabat; equation of state; high pressure; shock-wave compression.

References

1. Shanmin Wang, Yu Xiaohui, Zhang Y. et al. Crystal Structures, Elastic Properties, and Hardness of High-Pressure Synthesized CrB2 and CrB4. Journal of Superhard Materials, 2014, vol. 36, no. 4, pp. 279-287. DOI: 10.3103/S1063457614040066
2. Okamoto N.L., Kusakari M., Tanaka K. et al. Anisotropic Elastic Constants and Thermal Expansivities in Monocrystal CrB2, TiB2, and ZrB2. Acta Materialia, 2010, vol. 58, no. 1, pp. 76-84. DOI: 10.1016/j.actamat.2009.08.058
3. Hao Jiang, Zhao Xingbin, Hao Zhang et al. High-Pressure Synthesis, Mechanical Properties, and Magnetic Behavior of Chromium Diboride. AIP Advances, 2025, vol. 15, no. 5, pp. 1-10. DOI: 10.1063/5.0271239
4. Krutsky Yu.L. Raschet osnovnykh tekhnologicheskikh pokazateley protsessov samorasprostranyayushchegosya vysokotemperaturnogo sinteza tugoplavkikh soedinenii [Calculation of the Main Technological Parameters of Self-Propagating High-Temperature Synthesis Processes of Refractory Compounds]. Novosibirsk State Technical University, Novosibirsk, 2015. (in Russian)
5. Dik D.V., Gudyma T.S., Filippov A.A. et al. Reactive Hot Pressing of B4C-CrB2 Ceramics and Its Mechanical Properties. Journal of Applied Mechanics and Technical Physics, 2024, vol. 65, no. 2, pp. 249-256. DOI: 10.1134/S0021894424020068
6. Dik D.V., Filippov A.A., Burkhinova N.Y. Influence of the Microstructure Gradient on the Young Modulus and Hardness of B4C-CrB2 Ceramics Produced by Reactive Hot Pressing. Journal of Applied Mechanics and Technical Physics, 2025, vol. 66, no. 2, pp. 345-349. DOI: 10.1134/S0021894425020051
7. McQueen R.G., Marsh S.P., Taylor J.W. et al. The Equation of State of Solids from Shock Wave Studies. High-Velocity Impact Phenomena, 1970, vol. 293, no. 7, pp. 293-417. DOI: 10.1016/B978-0-12-408950-1.50012-4
8. Y. Zhang, K. Fukuoka., M. Kikuchi et al. Shock Compression Behaviour of Titanium Diboride. International Journal of Impact Engineering, 2005, vol. 32, no. 1-4, pp. 643-649. DOI: 10.1016/j.ijimpeng.2005.08.011
9. Grady D.E. Dynamic Properties of Ceramic Materials. Springfield, Virginia, 1995.
10. Kovalev Y.M., Magazov F.G., Shestakovskaya E.S. Quilibrium Mathematical Model of Multicomponent Heterogeneous Media. Bulletin of the South Ural State University. Series: Mathematics. Mechanics. Physics, 2018, vol. 10, no. 4, pp. 49-57. DOI: 10.14529/mmph180406
11. Maevskii K.K. Modeling of Shock-Wave Loading of Carbides as Mixtures of Components. Journal of Physics: Conference Series, 2021, vol. 2057, no. 1, 7 p. DOI: 10.1088/1742-6596/2057/1/012115
12. Dremin A.N., Karpukhin I.A. Metod opredelenija udarnyh adiabat dispersnyh veshhestv [Method of Determining the Shock Adiabats for Disperse Materials]. Journal of Applied Mechanics and Technical Physics, 1960, vol. 1, no. 3, pp. 184-188.(in Russian)
13. Dik D.V., Gudyma T.S., Filippov A.A. et al. Reactive Hot Pressing of B4C-CrB2 Ceramics and its Mechanical Properties. Journal of Applied Mechanics and Technical Physics, 2024, vol. 65, no. 2, pp. 249-256. DOI: 10.1134/S0021894424020068
14. Yadrenkin M.A., Fomichev V.P., Golyshev A.A. Features of Using a Railgun in Problems of High-Speed Interaction of Bodies with Obstacles. Journal of Technical Physics, 2024, vol. 94, no. 2, pp. 197-206.
15. Kraus A.E., Kraus E.I., Shabalin I.I. Programmnyy kompleks modelirovaniya protsessa dinamicheskogo vzaimodeystviya gomogennykh i geterogennykh deformiruemykh tverdykh tel ''Reactor3D'' Svidetel'stvo o registratsii programmy dlya EVM 2024684051, 2024.
16. Fomin V.M., Kraus E.I., Shabalin I.I. et al. Vysokoskorostnoe vzaimodeistvie geterogennykh materialov [High-Velocity Interaction of Heterogeneous Materials]. Novosibirsk, Siberian Branch of the Russian Academy of Sciences, 2025. (in Russian)
17. Buzyurkin A.E., Kraus A.E., Kraus E.I. et al. Determination of the Effective Dynamic Yield Strength of Heterogeneous Materials. Journal of Applied Mechanics and Technical Physics, 2024, vol. 65, no. 3, pp. 519-527. DOI: 10.1134/S0021894424030131
18. Kraus A.E., Kraus E.I., Shabalin I.I. Reactor 3D Software Performance on Penetration and Perforation Problems. Behavior of Materials under Impact, Explosion, High Pressures and Dynamic Strain Rates, 2023, vol. 176, no. 6, pp. 83-101. DOI: 10.1007/978-3-031-17073-7_6
19. Buzyurkin A.E., Kraus A.E., Kraus E.I. et al. Modeling the Response of Additively Manufactured Heterogeneous Metal-Ceramic Specimens to Dynamic Impact. Physical Mesomechanics, 2025, vol. 28, no. 1, pp. 27-42. DOI: 10.1134/S1029959924601118
20. Kraus A.E., Kraus E.I., Shabalin I.I. A Heterogeneous Medium Model and Its Application in a Target Perforation Problems. Multiscale Solid Mechanics. Advanced Structured Materials, 2021, vol. 141, article ID: 22, pp. 289-304. DOI: 10.1007/978-3-030-54928-2_22
21. Zaretsky E.B., Kanel G.I. The High Temperature Impact Response of Tungsten and Chromium. Journal of Applied Physics, 2017, vol. 122, no. 11, 11 p. DOI: 10.1063/1.4997674
22. Shuai Zhang, Heather D. Whitley, Tadashi Ogitsu. Phase Transformation in Boron Under Shock Compression. Solid State Sciences, 2020, vol. 108, article ID: 106376, 6 p. DOI: 10.1016/j.solidstatesciences.2020.106376
23. Kraus A.E., Buzyurkin A.E., Shabalin I.I. et al. Influence of Thin-Barrier Geometry on the Morphology of the Debris Cloud in Interactions with Space-Debris Fragments. Acta Astronautica, 2026, vol. 238, chapter B, pp. 569-581. DOI: 10.1016/j.actaastro.2025.10.023