Phase geometric propagation model of spherical projectile impacting thin plate based on shock wave propagation

Material phase-transition represents a significant phenomenon and mechanism in the context of hypervelocity protection. This study presents a thorough analysis of the phase-transition phenomena induced by shock pressure as the shock wave propagates initially to the rear of the projectile. The shock wave that induces a phase-transition is commonly referred to as a macroscopic phase-transition wave, whereas the interface that separates the distinct phases is referred to as macroscopic phase-boundary. The contact interface between the spherical projectile and the thin plate, characterized by its curved surface, plays a significant role in the nonlinear propagation and evolution of wave systems. The pressure distribution along the central axis of a spherical projectile is derived in accordance with the linear decay law observed for axial pressure. On this basis, a quadratic function is employed to characterize the trend of changes in wave front pressure, thereby facilitating the establishment of a model for wave front pressure distribution. Using the phase-transition pressure criterion for materials, the wave front phase evolution process is derived, and the macroscopic phase-boundary is determined. Based on the geometric propagation model (GPM) and the pressure distribution of the wave front, a phase geometric propagation model (PGPM) is proposed. The phase distribution of a spherical projectile impacting a thin plate is obtained by theoretical methods. The accuracy of the PGPM is subsequently validated through a comparison of its results with those obtained from numerical simulations.