Numerical Study On The Depth Of Penetration Into Concrete Targets By Projectiles

Concrete material has long played an important role in military and civil engineering constructions. Studies on penetration into concrete targets are quite necessary, especially in defense and nuclear engineering. Penetration into concrete target is a process with large strain, high strain rate, and high pressure, in which the dynamic responses of both the projectile and target are very complicated. Though many experimental and numerical investigations have been performed and a number of empirical formulations have been developed, there are special issues that need to be further studied. Numerical simulations is becoming more and more important, limited to the economic n and experimental conditions. In this paper, a series of simulations was performed using LS-DYNA to investigate dynamic spherical and cylindrical cavity expansion process of concrete materials. In addition, numerical simulations are performed to predict penetrations into concrete targets by non-deformable projectiles through AUTODYN-2D.Several empirical formulae for penetration depth, scabbing limit and perforation limit were introduced. The Forrestal's formula considering size effect obviously predicts the penetration depth for penetration experiments more effectively than the other empirical formulas do. Moreover, the application range of Forrestal's formula is considerably wider than those of the others; and every parameters in the model has clear physical meaning.A series of simulations was performed using LS-DYNA to investigate the dynamic spherical and cylindrical cavity expansion process of concrete materials. Results show that expansion velocity is significantly influenced by the expansion pressure, density, and compression strength of concrete, but is not affected by the initial radius of the cavity and the tensile strength of concrete. The relationship between expansion pressure and velocity was established based on numerical results. The equations were modified to calculate the penetration depth of rigid projectiles into concrete targets and then validated by experimental data. The critical pressure of cylindrical cavity expansion is lower than that of spherical cavity, whereas radial stress in the response regions is high under the same pressure. For impact velocity lower than the critical velocity, the penetration depth obtained from the cylindrical cavity expansion model is higher than that from the spherical cavity expansion model and is closer to the experimental data. For impact velocity higher than the critical velocity, the penetration depth obtained from the cylindrical cavity expansion model is low and the calculation error is high. This work provides a basis for selecting when to use spherical cavity expansion over cylindrical cavity expansion to predict the final penetration depth of rigid projectiles into concrete targets.In addition, numerical simulations are performed to predict penetrations into concrete targets by non-deformable projectiles through AUTODYN-2D. The results of both the numerical simulation and empirical approaches are consistent with the measured experimental data; the numerical outcomes indicate that deceleration is dependent on the shape of the projectile nose, concrete target strength and impact velocity. Moreover, the inertial term accounts for a large proportion of the deceleration when initial impact velocity increases. A new target model was established with a pre-drilled hole around the symmetry axis to simulate the entrance effect of the crater phase on the entire penetration process. The depth of penetration into a concrete target with a pre-drilled hole is significantly lower than that into a regular target. The entrance effect diminishes with an increase in impact velocity. In addition, simulation results indicate that nose shape significantly affects crater region depth, although this depth is independent of the strength of the concrete target and the impact velocity. The crater region depths determined through simulation enhance the accuracy of both the numerical and empirical approaches in terms of predicting the penetration depths for concrete targets impacted by projectiles with different nose shapes.