The metallic targets are regarded as the compressible power-law strain-hardening materials, and the resistance function coefficients for three kinds of steel and 11 kinds of aluminum targets are obtained based on the spherical cavity-expansion theory. Then, an explicit expression for projectile impact resistance is proposed by curve-fitting, which is simple to use without performing the complex numerical solution. For the projectile perforating on the finite thickness plate, the free-surface effect is realized by multiplying a decay function with the above explicit resistance. Furthermore, a new phenomenological perforation model considering the projectile entry and exit phases, compressibility, rear free-surface and fracture effects of target is established, which is sufficiently verified by comparing with the existing 19 sets of projectile perforation tests and two typical theoretical models. Finally, the influence of the impact velocity on the rear free-surface effect is discussed.
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