Improved shaped charge formation model based on the effective charge

Shaped charges, renowned for their exceptional penetration capabilities, play a critical role in military and civilian applications, including armament manufacturing and petroleum extraction. However, traditional jet formation models exhibit limited accuracy, particularly in failing to capture the reverse velocity gradient observed at the jet tip. To address these limitations, this study innovatively developed a dynamic effective charge (DEC) model, building upon the established one-dimensional quasi-steady jet formation theory (PER theory). Specifically, an effective charge calculation method was developed to accurately determine the portion of explosive charge actively driving the collapse of the shaped charge liner. Additionally, a dynamic acceleration model was incorporated to realistically characterize the liner's collapse process. Through these advancements, the DEC model not only enables accurate predictions of jet velocity but also effectively captures the reverse velocity gradient phenomenon at the jet tip. Moreover, the DEC model explains the nonlinear relationship between the jet velocity and the charge length-to-diameter ratio, revealing that there is a limiting value of the shaped charge length to diameter ratio, beyond which additional increases in charge length result in minimal velocity enhancements. These advancements provide critical theoretical insights and practical guidelines for optimizing shaped charge designs across a broad range of engineering applications.