Modeling of temporary cavity in ballistic gelatin based on spherical cavity expansion model

• Published in: Proceedings of the Institution of Mechanical Engineers. Part C, Journal of mechanical engineering science Journal of mechanical engineering science, 2023-12, Vol.237 (23), p.5559-5570
• Main Authors: Liu, Li, Yang, Xiao-Yi, Huang, Yu, Wang, Peng-Fei, Zuo, Qiang
• Format: Article
• Language: English
• Subjects: Ballistic penetration; Cavity expansion; Differential equations; Energy conversion; Gelatin; High speed; Projectiles; Size effects
• ISSN: 0954-4062; 2041-2983
• DOI: 10.1177/09544062231167029

To investigate the expansion mechanism of the temporary cavity produced by high-speed penetrators into ballistic gelatin, a dynamic spherical-cavity-expansion model for gelatin targets was proposed with consideration of the outer boundary size. The theoretical solution of the cavity radial stress was obtained and the energy conversion and conservation relation during the cavity expansion process was established. The influence of the finite boundary to the solutions of the cavity radial stress and the deformation energy in the medium was analyzed. The energy conversion and conservation relation was applied to penetration process of high-speed penetrators into soft targets and regarded as the temporary cavity expansion model. This model is a nonlinear first order differential equation about the cavity radius, which can be solved numerically to obtain the variation of temporary cavity volume with time. Experimental results of high-speed penetrators (bullets and fragment simulating projectile with different shapes) penetrating into ballistic gelatin were analyzed. Temporary cavity results of rhombic fragment simulating projectiles were used to estimate the parameters in the model. Then, model predictions were compared with the temporary cavity results of bullets, spheres and cylinders to verify the reliability of the model. It was found that: (1) if the ratio of the cavity radius to the initial target boundary radius exceeds 0.62, the error caused by ignoring the boundary size effect will exceed 10%; (2) Model predictions for temporary cavity volume of penetration produced by various penetrators are shown to be in good agreement with the corresponding experimental results.