A spherical cavity expansion model for penetration of ogival-nosed projectiles into concrete targets with shear-dilatancy

A dynamic spherical cavity-expansion penetration model is suggested herein to predict the penetration and perforation of concrete targets struck normally by ogivalnosed projectiles.Shear dilatancy as well as compressibility of the material in comminuted region are considered in the paper by introducing a dilatant-kinematic relation.A procedure is first presented to compute the radial stress at the cavity surface and then a numerical method is used to calculate the results of penetration and perforation with friction being taken into account.The influences of various target parameters such as shear strength,bulk modulus,density,Poisson＇s ratio and tensile strength on the depth of penetration are delineated.It is shown that the model predictions are in good agreement with available experimental data.It is also shown that the shear strength plays a dominant role in the target resistance to penetration.

Finite Spherical Cavity Expansion Method for Layering Effect

A decay function for the layering effect during the projectile penetrating into layered targets is constructed, which is obtained via the theoretical solution of a dynamically expanding layered spherical cavity with finite radius in the layered targets that are assumed to be incom- pressible Mohr-Coulomb materials. By multiplying the decay function with the semi-empirical forcing functions that account for all the constitutive behavior of the targets, the forcing functions for the layered targets are obtained. Then, the forcing functions are used to represent the targets and are applied on the projectile surface as the pressure boundary condition where the projectile is modeled by an explicit transient dynamic finite element code. This methodology is implemented into ABAQUS explicit solver via the user subroutine VDLOAD, which eliminates the need for discretizing the targets and the need for the complex contact algorithm. In order to verify the proposed layering effect model, depth-of-penetration experiments of the 37 mm hard core pro-jectile penetrating into three sets of fiber concrete and soil layered targets are conducted. The predicted depths of penetration show good agreement with the experimental data. Furthermore, the influence of layering effect on projectile trajectory during earth penetration is investigated. It is found that the layering effect should be taken into account if the final position and trajectory of the projectile are the main concern.

PREDICTION OF PROJECTILE PENETRATION AND PERFORATION BY FINITE CAVITY EXPANSION METHOD WITH THE FREE-SURFACE EFFECT

With a target treated as the incompressible Tresca and Mohr-Coulomb material, by assuming that cavity expansion produces plastic-elastic and plastic-cracked-elastic response region, the decay function for the free-surface effect is constructed for metal and geological tar- gets, respectively. The forcing function for oblique penetration and perforation is obtained by multiplying the forcing function derived on the basis of infinite target assumption with the de- cay function. Then the projectile is modeled with an explicit transient dynamic finite element code and the target is represented by the forcing function as the pressure boundary condition. This methodology eliminates discretizing the target as well as the need for a complex contact algorithm and is implemented in ABAQUS explicit solver via the user subroutine VDLOAD. It is found that the free-surface effect must be considered in terms of the projectile deformation, residual velocity, projectile trajectory, ricochet limits and critical reverse velocity. The numerical predictions are in good agreement with the available experimental data if the free-surface effect is taken into account.

Resistance of grid steel-tube-confined concrete targets against projectile impact: Experimental investigation and analytical engineering model

Steel-tube-confined concrete(STCC) targets are provided with excellent anti-penetration performance over semi-infinite concrete(SIC) targets since the steel tube imposes passive restraint on the in-filled concrete during the penetration process. Grid STCC system with square steel tubes is a potential solution to protective structures. In this paper, experiments of 9-cell grid STCC targets penetrated by 12.7 mm Armor Piercing Projectile(APP) were performed. The influence of side length and thickness of steel tube,steel ratio and impact velocity on anti-penetration performance were taken into account. Additionally,single-cell square STCC targets were also designed and tested for comparison with the 9-cell grid STCC targets. Damage modes and parameters of the tested targets were measured and discussed. Moreover,the stiffness of radial confinement of grid STCC targets is achieved according to the elastic solution of infinite cylindrical shell in Winkler medium. Furthermore, the penetration resistance and depth of penetration(DOP) for grid STCC targets are obtained on the basis of the dynamic finite spherical cavityexpansion(FSCE) models including radial confinement effect. It is shown that the 9-cell grid STCC targets with optimal dimension match of thickness and side length of steel tube can reduce the DOP by about17 % and 23 % in comparison with the SIC targets and single-cell square STCC targets, respectively, due to both the confinement of square steel tube to concrete in the impacted cell and the additional confinement of the surrounding cells to the impacted cell;the penetration resistance and DOP of the grid and cellular STCC targets with similar steel ratio is close, and thus the grid STCC targets with simpler manufacturing process and excellent in-plane expandability are preferred in engineering practice;moreover, the predicted results of DOP model based on the FSCE models agree well with the tested results with the maximum disparity less than 12 % and the proposed model is more applicable to the grid and cellular STCC targets with high radial confinement.