Abstract：To address the limitations of existing engineering models for penetration depth that inadequately account for the coupling between the impact-induced energy release reaction of metal-based energetic jets and penetration behavior, a novel engineering model for penetration depth was developed. The model was based on a detailed analysis of the physical process of energetic jet penetration into steel targets, combined with the dynamic features of the impact-induced energy release. The model aimed to improve prediction accuracy for steel targets under impact conditions encountered in shaped charge applications. The quasi-steady theory of ideal incompressible fluid mechanics was adopted to describe fluid-like jet behavior. A jet transient reaction time was introduced as a key parameter to capture the timescale of chemical energy release relative to the penetration event. The model systematically incorporated the staged effects of peak overpressure arrival time and the evolving strength of both jet and target materials. Analytical expressions were derived to link penetration depth with jet properties, jet transient reaction time, and target resistance, providing a quantitative framework for performance prediction. Model parameters were calibrated using experimental measurements. Based on this framework, the influence of jet transient reaction time on penetration depth was investigated. Results show that penetration depth first increases and then decreases as reaction time extends. This nonlinear trend indicates that neither very short nor excessively long reaction times are favorable for maximizing penetration. Experimental validation was performed; results show that model predictions deviate by less than 10 percent from measured penetration depths under multiple test conditions, confirming the model's accuracy. The proposed model provides new theoretical insight into the coupling between penetration mechanics and impact-induced energy release of metal-based energetic jets. It also offers practical guidance for the structural optimization of shaped charges and supports the quantitative assessment of damage to armored targets, showing potential value for both defense applications and engineering design.
2025, Vol. 46 
