The projectile deflects and even ricochets after an oblique impact on the concrete. However, research on the oblique impact of projectiles on concrete targets mainly focuses on oblique penetration and the critical ricochet angle, and there are few experimental studies on ricochets. Deflection and its influencing factors remain undefined. This study conducted experiments and LS-DYNA numerical simulations on projectiles obliquely impacting C60 concrete targets. The experimental research visually revealed deflection and ricochet phenomena after the oblique impact. The ricochet caused by large-angle impacts can effectively reduce the damaged area of concrete targets. Subsequently, the main governing parameters affecting the deflection angle of the projectile were identified through dimensional analysis, and a sensitivity analysis was performed on these parameters using an orthogonal experimental design. On this basis, the influence of the incident angle, impact velocity, and projectile length-to-diameter ratio on the projectile deflection was further clarified. The results showed that the maximum deflection angle was achieved when a 30 mm caliber projectile obliquely impacted a C60 concrete at an incident angle of ∼45°. In the case of ricochets, the deflection angle increased with an increase in the impact velocity and decreased with an increase in the length-to-diameter ratio. This study aids in predicting and controlling projectile deflection and provides a reference for the innovative design of concrete protective structures.

The ricochet phenomenon has been studied worldwide for a long time in consideration of its significance in ballistics. A ricochet projectile has proven to be worthless to its launcher, as warheads fail to penetrate the interior of targets and strike the facilities and personnel of enemies effectively. A large portion of related research has been dedicated to avoiding ricocheting, which mainly focuses on improving the penetration ability of a projectile in order to obtain a better penetration effect, while investigations on the proactive protection of key targets from damage caused by a ricochet projectile are minor. This study analytically explores the ricochet range of a projectile obliquely penetrating a thick steel target. Firstly, the moment of momentum equation of the ricochet projectile based on theoretical mechanics is utilised to analytically calculate its trajectory, where a mathematical model of a two-stage ricochet impacting is established through the geometrical analysis of the ricochet process for determining the ricochet range of a projectile and the size of the bulletproof structure. Then, impact experiments of a projectile obliquely penetrating thick steel targets at different striking velocities and inclination angles are carried out, and the influences of the striking velocity and angle of attack on the damage pattern, area and penetration depth are discussed to identify the ricochet phenomenon. Moreover, the deflection angle of the ricochet projectile is computed, which is compared with the experimental measurements in order to validate the accuracy of this proposed model. This proposed research may promote security protection during live-firing training and provide a theoretical foundation for the optimisation of purposeful protection.

From an offensive point of view, increasing the impact velocity of the projectile is an effective way to enlarge its penetration depth. However, as the projectile penetrates the target, there often exists an angle of attack, the resultant force on the projectile is in a different direction from that of projectile velocity, which causes the deflection of the projectile, and thus the strike effect is greatly weakened. From the other perspective, the deflection of the projectile can contribute to proactive protection of key targets from damage caused by a deeper penetration which has been an important consideration for actual protective structure. Presently, investigations on the deflection mechanism of the impact projectile are relatively few, and there is especially a lack of more comprehensive theoretical and experimental studies. In this paper, the mechanism of projectile deflection when penetrating a composite concrete target is thoroughly analyzed. The composite concrete target composed of a concrete fixed target and multiple diamond-shaped moving targets, similar to the structural system for multi-layer overlay extension, showed better anti-penetration performance in practical protective structures. The analytical model of projectile deflection during penetrating the target is established through simultaneously resolving the dynamic equations for the projectile and moving target. Penetration tests of the composite concrete target plate impacted by a 76 mm projectile were conducted to examine the effectiveness of the analytical model, where impact velocity and point and the size of the moving target were considered. On this basis, the influences of impact velocity and point on the deflection of the projectile are disclosed, and the effects of parameters of moving target are discussed. These findings can provide significant references for optimization of advanced protective structures and improvement of their anti-penetration performance.

Explosively formed projectile (EFP) has the advantages of high flight speed, high burst height, insensitivity to initial velocity, etc. To study the forming performance of multiple explosively formed projectile (MEFP) and to analyze the factors influencing the forming results. A directional pentagonal prism MEFP with five liners is proposed in this paper. Experiments were conducted to validate the performance of this MEFP. The experimental results show that the generated EFPs have high flight speeds. However, the EFP hit position on the target plate was offset, causing multiple positional penetrations. To analyze the causes of the phenomenon, a numerical simulation model of directional MEFP is established and the forming process of MEFP is numerically simulated. The simulation results indicate that the EFP fracture occurs during the forming process due to the asymmetric detonation wave, and its tail cannot be fully closed. Combined with the numerical simulation and experimental results, the forming performance of the liners used in the MEFP has been further developed. Further analysis was carried out on the effect of liner thickness and height on forming performance. It can be seen that as the thickness of the liners increases, the length of the head of EFP increase, the incidence of EFP tail fracture decreased, the aspect ratio increases and the EFP velocity decrease. As the height of the MEFP increases, the velocity of the EFP increases, the head ratio increases, the shape of the detonation wave tends to be symmetrical, and the tendency of the EFP to appear as an unclosed tail decreases.

Viscoelastic artificial boundary elements are one of the most commonly used artificial boundaries when solving dynamic soil-structure interactions or near-field wave propagation problems. However, due to the lack of clear and practical stability criteria for the explicit algorithm that considers the influence of viscoelastic artificial boundary elements, the determination of the stable time increment in such numerical analyses is still a challenge. In this study, we proposed a numerical stability analysis method for the explicit algorithm with a 3D viscoelastic artificial boundary element based on the idea of a subsystem. Through this method, the artificial boundary subsystem that controls the stability of the overall numerical system is determined, and the analytical solution for the stability condition of the explicit integration algorithm with 3D viscoelastic artificial boundary elements is obtained. On this basis, the maximum time increment for solving dynamic problems with viscoelastic artificial boundary elements can be determined.

A quasi-static finite cavity cylindrical expansion model is proposed to investigate the lateral boundary effect during long-rod penetration. Analytical solutions for the cavity pressure in the elastic–plastic stage and plastic stage are obtained, through which a decay function for the lateral boundary effect is constructed. The resistance of the target with finite diameter R_T is obtained by multiplying the decay function with the resistance of infinite target R_T*. Then, a theoretical model for the penetration into the metal targets with finite diameters by long rods is proposed by substituting R_T into the Alekseevskii–Tate model. The proposed model is verified by comparison with existing experimental results. Furthermore, the effect of the target diameter, initial impact velocity and yield criterion on the penetration depth and resistance are investigated. The results showed that the lateral boundary effect should be taken into account if the ratio of the target radius to the rod radius (r_t0/R_P) is less than 25.