Ballistic Equivalent Thickness Analytical Theory for Ductile-Hole-Growth Metal Targets Penetrated by Ogive-Nose Armor-Piercing Projectiles

Abstract

In armor lightweighting design and damage efficacy assessment, the determination of ballistic equivalent thickness constitutes a critical challenge. Conventional methodologies predominantly employ fixed strength ratio approaches and curve fitting techniques, but fail to account for the synergistic effects of strength dissipation and plastic hardening during the penetration process, resulting in substantial deviations in thickness equivalent conversion results under varying projectile operating conditions. Cavity expansion theory has been thoroughly validated in the domain of ballistic limit velocity prediction; however, no study has yet performed an inverse derivation based on this theory to establish the ballistic equivalent correlation between different target plates. In this paper, based on the compressible cavity expansion theory, a rigorous mathematical inversion derivation is performed to derive an explicit analytical formula for the ballistic equivalent thickness of ductile metallic target plates struck by ogive-nose armor-piercing projectiles. Leveraging an authoritative open-access ballistic test database, over 950 independent penetration equivalent conditions are screened to complete model validation. The results demonstrate that the proposed model achieves a mean absolute percentage error of 7.4% for ductile-hole-growth metals with zero empirical calibration, exhibiting prediction accuracy and correlation significantly superior to conventional empirical power-law models. Theoretical analysis reveals that under conditions where inertial effects are negligible, the equivalent thickness ratio between different ductile metallic target plates is independent of projectile geometry, density, mass, and other parameters, being determined solely by the quasi-static cavity expansion resistance of the two materials. The equivalent thickness conversion relationship established in this paper eliminates the reliance on case-by-case experimental calibration inherent in traditional approaches, providing a rigorously traceable theoretical foundation for quantitative equivalent selection of armor materials and lightweight protective structure design, and can be directly applied to equivalent substitution testing and engineering optimization design of armored vehicle and naval ship protective plates.