Abstract

Accurately predicting the terminal state of shaped charge jets (SCJs) is crucial for optimizing their penetration performance. The core challenge lies in a deep understanding of the complete physical chain from shock compression to unloading expansion. This paper presents a hybrid analytical–numerical model for SCJ formation that incorporates a shock-pressure-driven unloading term. Unlike classical PER theory, the proposed model explicitly introduces an unloading term and derives a quantitative expression for the momentum conversion factor (ΠDMCF) to quantitatively characterize the momentum redistribution during collapse. Our analysis finds that ΠDMCF exhibits a typical S-shaped evolution law as the dimensionless Mach number (Ma) varies. This study uses a logistic function with two characteristic parameters, Ma0 and k, to accurately fit the data. The research results indicate that the model parameters have clear physical connotations: Ma0 characterizes the critical condition for the material to transition from “strength-dominated” to “kinetic-energy-dominated” behavior, while k reflects the degree of abrupt transition. After calibrating the model parameters using high-fidelity numerical simulations, the jet morphology and velocity data obtained from X-ray flash photography experiments are compared and verified, confirming that the model can significantly improve the prediction accuracy. Especially for Ti55Al20V5Zr5Nb15 HEA, the prediction error in the jet velocity is less than 4%, and the theoretically predicted shock pressure is highly correlated with the numerical results (R2 = 0.943). A further mechanistic analysis indicates that the proposed model successfully decodes the unique response of the HEA: its high dynamic strength results in a larger value, causing its momentum conversion efficiency to fall within a lower range under typical impact conditions. The theoretical framework constructed in this study provides a hybrid analytical–numerical and highly reliable theoretical tool for the accurate prediction of SCJs, as well as for the material selection and design of high-performance liners.

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