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• Reason of the scaling effect of rigid projectile penetration into concrete target is clarified. • Generation algorithms of 3D mesoscopic concrete models are proposed. • Compared to the homogeneous concrete model, the scaling effect is reproduced numerically based on the verified 3D mesoscopic concrete model. • The parametric analyses show that the maximal 26% deviations for predicting DOP can be induced when the scaling effect is considered or not. The scaling effect of rigid projectile penetration into concrete target should be paid great attention in ballistic performance evaluation of earth-penetration-weapon and design of protective structures, and this paper aims to discuss the scaling effect based on the three-dimensional (3D) mesoscopic concrete model. Firstly, by evaluating the existing typical (semi-)empirical formulae and penetration tests, it is found that the scaling effect is mainly attributed by the inconsistent variations of projectile diameter and coarse aggregates size in the scaled impact tests. Secondly, based on MATLAB, the generation algorithms of 3D mesoscopic concrete models with the randomly distributed sphere and convex polyhedron coarse aggregates are proposed, respectively. The influences of two coarse aggregates shapes on the compressive strength and impact resistance of concrete target are further discussed, and the sphere coarse aggregates are adopted to guarantee both the calculation accuracy and efficiency. Then, based on five sets of projectile penetration/perforation tests on concrete targets, the 3D mesoscopic concrete model with randomly distributed sphere coarse aggregates and the corresponding constitutive parameters are validated numerically by LS-DYNA. Finally, the scaling effect is reproduced numerically based on the verified 3D mesoscopic concrete model. The influences of projectile diameter, volume fraction and size of coarse aggregates on the scaling effect are further assessed. In the discussed scenarios, the maximal 26% deviations for predicting depth of penetration (DOP) can be induced when the scaling effect is considered or not. [ABSTRACT FROM AUTHOR]

Highlights • A series of rigid projectile penetration tests on concrete targets pre-damaged by explosively formed projectile (EFP) is conducted. • Impact performance of the individual rigid projectile and two-stage munitions, as well as the influences of concrete type, projectile striking velocity and target configuration are experimentally studied. • Penetration process of the following rigid projectile into the pre-damaged target is numerically reproduced with the restart input data method implemented in the finite element program LS-DYNA. • Influences of the liner material and configuration of shaped charge, as well as the rigid projectile diameter on the impact performance of two-stage munitions are further discussed. Abstract The two-stage munitions is newly utilized to attack the hard and deeply buried protective structures, while the related work on the impact performance of two-stage munitions into concrete targets is still limited. This paper addresses the impact performance of one typical two-stage munitions, which consists of a precursor explosively formed projectile (EFP) and a following rigid projectile. Firstly, based on our previous EFP impacting test on the concrete targets (Hu et al., IJIE, 2017), a series of rigid projectile penetration tests on these pre-damaged concrete targets is further conducted. By assessing the dimensions of the penetration boreholes, the influences of concrete type (normal strength concrete (NSC) and reactive powder concrete (RPC)), target configuration (monolithic and spaced) and rigid projectile striking velocity (300 m/s–500 m/s) on the targets damage subjected to the two-stage munitions are experimentally discussed. Then, by adopting the restart input data method implemented in the finite element (FE) program LS-DYNA, the targets damage subjected to the precursor EFP is recorded and the penetration process of the following rigid projectiles into the pre-damaged targets is numerically reproduced. Finally, based on the validated restart input data method, material models and the corresponding parameters, the impact performance of the two-stage munitions with different liner materials (T2 copper and 2A12 aluminum) and configurations (spherical segment, conic and truncated) of shaped charge as well as the following rigid projectile diameters (0.1∼0.9 times the shaped charge diameter) is further discussed, respectively. [ABSTRACT FROM AUTHOR]

Since penetration tests of concrete targets against rigid projectiles are commonly conducted in reduced geometrical scale, whether the replica scaling law holds or not is very important for extending the knowledge based on the small-scale experiments to the large-scale or prototype penetration scenarios. In this paper, based on the available experimental data for depth of penetration (DOP) and discussions on the empirical formulae, it is verified that the replica scaling law is satisfied for DOP in rigid projectile penetrations, as long as the scaling is done strictly for both projectiles and concrete targets including the coarse aggregates. And the coarse aggregates with invariant size (not replica-scaled) could account for the non-scaling effect in DOP found in tests and empirical formulae. To explore the non-scaling effect in DOP caused by aggregates, a 3D mesoscopic finite element model for concrete target is developed. Based on the parametric analyses, it indicates that, the magnitude of the non-scaling effect decreases with the increasing of the cement strength when the aggregate strength is fixed. While the influence of the aggregate strength on the non-scaling effect is not so obvious comparing with the influence of cement strength. Besides, the magnitude increases with the increasing of the volume fraction of aggregates. These conclusions imply that, the non-scaling effect in DOP for different concrete targets with the same magnitude implied by the empirical formulae, and the always held scaling law in the (semi-)analytical models, may be unreasonable. Finally, based on the numerical results, a semi-analytical model for predicting DOP is proposed, which improved our previous model by further considering the non-scaling effect. [ABSTRACT FROM AUTHOR]

Terminal ballistic performance of high-strength projectiles penetrating into metallic targets is mostly concerned by both weapon and armor designers. Most existing works are concentrated on the rigid-eroding penetration regime, and limited studies have addressed the rigid-deforming-eroding penetration regime. In this paper, nineteen shots of hemispherical nosed D6A steel projectiles penetration test on 5A06-H112 aluminum targets is conducted with a wide range of velocities (696 m/s–1870 m/s). The non-monotonic dependence of depth of penetration (DOP) on the impact velocity is observed, which successively corresponds to the three penetration stages, i.e., rigid projectile penetration, deforming projectile penetration without eroding and eroding projectile penetration. Then, for the non-monotonic rigid-deforming-eroding projectile penetration regime, the applicability of the existing six classical theoretical models for both rigid and eroding projectile penetrations is evaluated. Furthermore, the transition velocities (the upper limit of rigid penetration and the lower limit of eroding penetration) are discussed and an empirical judgement criterion for the occurrence of non-monotonic dependence is proposed. Finally, by conducting the dynamic compression test, quasi-static tension test under varying temperature, etc., the Johnson-Cook model parameters for the present target and projectile are calibrated and validated by numerically simulating the present test. [ABSTRACT FROM AUTHOR]

A hyperbolic yield criterion and Murnaghan equation of state were introduced to describe the plastic behavior of concrete material under projectile penetration, and an extended dynamic cavity expansion model was proposed. Then, a unified one-dimensional resistance of concrete target to projectile penetration was formulated, in which the projectile nose shape influences were taken into account by three non-dimensional coefficients. Furthermore, combined with the Newton's second law and Alekseevskii-Tate equations, both rigid and eroding projectile penetration models into concrete targets were established. By comparing with the existing tests data as well as prediction results of previous model based on the linear yield criterion and equation of state, the proposed models were verified. Besides, a series of practical parameters of hyperbolic yield criterion and Murnaghan EOS for the extended dynamic cavity expansion model were given and verified. [ABSTRACT FROM AUTHOR]

Ultra-high performance cement based composite (UHPCC) has prominent projectile impact resistance. Aiming to theoretically predict the depth of penetration for rigid projectile penetrating UHPCC target, an improved dynamic cavity expansion model was proposed to describe the plastic behavior of UHPCC material under projectile penetration with a hyperbolic yield criterion and nonlinear equation of state (EOS). Then, combined with the Newton’s second law, rigid projectile penetration model into UHPCC target was established, which was verified by comparing with the previous penetration test data, classic empirical formula and prediction of previous cavity expansion model based on linear yield criterion and EOS. Besides, a series of practical parameters of the hyperbolic yield criterion and nonlinear EOS for the improved dynamic cavity expansion model were given and validated. [ABSTRACT FROM AUTHOR]

Two models were proposed in this note. Firstly, by assuming that the resistance acting on the projectile keeps unchanged during the penetration process, the new mean resistance approach based on dynamic cavity-expansion approximation was proposed. A simple unified model was further given to predict the depth of penetration (DOP) of different nose-shaped hard projectiles penetrating into diversified targets (e.g. concrete, metal, rock). Besides, the related mean resistance coefficient was confirmed as 0.4 based on the parametric analyses. Secondly, an experiment-based simplified semi-analytical perforation model for the thick concrete slab was obtained, in which the rear crater height was suggested as 2.5 times of the projectile diameter, and the ejecting velocity of rear shear fragment was advised as 20% of the residual velocity of projectile after perforation. The existing method for predicting the rear crater height was improved and the kinetic energy carried by the rear scabbing fragments were considered quantitatively. Finally, by comparing with the available test data, the prediction accuracy for DOP and residual velocity as well as the concise expressions of our models were validated. [ABSTRACT FROM AUTHOR]