The effects of compressibility and target strength on shaped charge jet penetration

The penetration of shaped charge jets into targets at high velocities is significantly influenced by the compressibility effect, while at low velocities, the strength effect becomes predominant. In the latter regime, material strength dictates the resistance to plastic deformation and flow, a contrast to the shockwave-dominated interactions where compressibility is key. This paper presents a self-consistent compressible penetration theory that considers both the axial penetration and radial crater growth of shaped charge jets into targets. An integrated approach where the axial and radial dynamics are coupled has been proposed, influencing each other through shared physical principles rather than being treated as separate, empirically linked phenomena. The presented theory is rooted in the compressible Bernoulli equation and the linear Rankine–Hugoniot relation. These foundational equations are employed to accurately model the high-pressure shock state and subsequent material flow at the jet-target interface, providing a robust physical basis for the penetration model. Notably, it considers the target material's compressibility, which elevates the pressure at the jet-target interface beyond that observed with incompressible materials. This pressure increase is directly proportional to the target's degree of compressibility. As such, this model of compressible penetration reorients the analytical approach: rather than merely estimating penetration resistance, it determines this value from the target material's specific compressibility and yield strength. This shift from empirical correlations to a physics-based derivation of penetration resistance enhances the model's predictive power, particularly for novel target materials or engagement conditions outside established experimental datasets. This investigation establishes a quantitative link between the material's yield strength and its penetration resistance. The accuracy of this penetration resistance value is paramount, as it significantly influences the predicted crater diameter; indeed, the crater diameter's sensitivity to this resistance underscores the necessity for its precise determination. Ultimately, by integrating the yield strength of the target material, this framework enables the prediction of both the penetration depth and the resultant crater diameter from a shaped charge jet. The theory's validation involved two experimental sets: the first focused on shaped charge jet penetration into 45# steel at varied stand-offs, while the second utilized targets of high-to ultrahigh-strength steel-fiber reactive powder concrete (RPC) with differing strength characteristics. These experimental campaigns were specifically chosen to test the theory against both ductile metallic alloys, where plastic flow is significant, and advanced quasi-brittle cementitious composites, presenting a broad spectrum of material responses and penetration challenges. Resulting hole profiles derived from theoretical calculations demonstrated a strong correspondence with empirical measurements for both material types.