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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.

Investigations of the large commercial aircraft impact effect have been drawing extensive attention, and the detached massive engine during aircraft collision would cause severer local damage to structures than the aircraft fuselage. Ultra high performance steel fiber reinforced concrete (UHP-SFRC) is an excellent material for the construction of valuable infrastructures to resist the intensive loadings. This paper aims to study the impact resistance of UHP-SFRC panels subjected to the aircraft engine. Firstly, a series of reduce-scaled engine model perforation test was conducted, in which the residual velocities of the engine missiles as well as the damage of both engine missile and target slab were derived and assessed. Then, a mesoscopic model of UHP-SFRC considering the random distribution, volumetric ratio, as well as the bonding and slipping effects of the fibers was established. By using the finite element program LS-DYNA and comparing with the macroscopic homogenous approach, the present test was better reproduced by the mesoscopic approach. Furthermore, based on the parametric analyses of panel thickness and engine missile impact velocity, a modified empirical formula for predicting the engine missile residual velocity was presented to guide the design of protective structures.

It is very necessary to predict the residual velocity of a projectile after perforating a concrete barrier for the protective structures. In this paper, projectile perforation test on the thin 128.4 MPa ultra-high performance steel fiber reinforced concrete (UHP-SFRC) slabs was conducted, in which the diameter of projectile was 25.3 mm and the thicknesses of slabs ranged from 40 mm to 100 mm. All the slabs were perforated normally and the projectile residual velocities were captured by high-speed camera. To assess the projectile residual velocity, a semi-analytical projectile perforation model for thin concrete slab ( H / d ≤ 5) was established, which completes our previous work [Peng et al., 2015] for thick slab ( H / d > 5) within a unified framework. The proposed model was validated by the present and existing available perforation test data on thin concrete slab. Furthermore, the unified model was employed to evaluate the impact resistance of spaced segmented concrete slabs and good agreements were achieved.

The basalt aggregated ultra-high performance steel fiber reinforced concrete (UHP-BASFRC) was prepared and cured atmospherically, which totally fits the requirement of the on-site constructions. By designing a new type of sabot and confirming the optimal sabot length, the sub-caliber experiment of flat nosed projectile penetrating into 128.4 MPa UHP-BASFRC target was carried out. The 15 mm-diameter cylindrical 45CrNiMoV steel projectiles were launched by the 25.3 mm caliber powder gun with striking velocities from 299 m/s to 842 m/s. Damage of the target was assessed and the distinguished protective performance of UHP-BASFRC target was validated. In the present test, both rigid and erosive projectile penetrations occurred and the depth of penetration under above two regimes were discussed respectively. Rigid projectile penetration depth was quantitatively evaluated by the existing models, while the erosive projectile penetration depth was predicted by the combination of cavity expansion theory and Alekseevskii–Tate equation. For UHP-BASFRC target, our previously proposed rigid penetration and the present established erosive penetration models were validated.

For the constructions of protective structures against potential projectile high-speed impact, the optimal ultra-high performance cement based composite (UHPCC) (straight steel fiber with the volumetric ratio of 2%, high-strength basalt aggregates with the size range of 5-10 mm, the designed uniaxial compressive strength of ∼ 100 MPa) was prepared. By casting two batches of 50 mm × 100 mm cylindrical UHPCC specimens with the uniaxial compressive strengths of 95 MPa and 129 MPa, the triaxial compressive behavior of UHPCC under high confining pressure (up to 100 MPa) was experimentally studied. Based on the deviatoric stress-strain curves under various confining pressure, the failure criteria and toughness of UHPCC under triaxial compression were discussed. At last, the dominant strength parameters of Holmquist-Johnson-Cook constitutive model were confirmed based on the present and existing triaxial compression tests on high-strength concrete. The validity of which was verified based on eleven sets of projectile penetration or perforation tests on concrete-like targets with the uniaxial compressive strength ranged from 60 MPa to 157 MPa.

Aiming to protect person and equipment in the protective structures against high-speed small caliber arms, the optimal basalt aggregated ultra-high performance steel fiber reinforced concrete (UHP-BASFRC) with good workability was designed and prepared at ambient temperature and pressure. Prototype impact test of 19 bare and rear fabric (CFRP or UHMWPE) strengthened UHP-BASFRC panels (40–130 mm thick) struck by 7.62 mm armor-piercing incendiary (API) bullets with velocities of 810 m/s was conducted. Perforation limit of the bare UHP-BASFRC panel was experimentally confirmed and the distinguished protective performance of bare and fabric strengthened UHP-BASFRC slabs was validated. Rear fabric strengthening could decrease the perforation limit, considerably reduce the rear crater and block the rear ejected fragments, and CFRP fabric performed better than UHMWPE fabric. Besides, a practical approach to predict the terminal ballistic parameters of bullet impacting on both the traditional no coarse aggregated UHP-SFRC and the present UHP-BASFRC slabs was suggested.

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.

The aircraft impact force directly influences the local failure and global response of the nuclear power plant (NPP) containment, while the existing theoretical models and the field tests were almost based on the flat target. In order to analyze the radius effect of the circular sectional containment on the impact force, a fine FE model of the commercial aircraft A320 was established and validated by the available limited full-scale F-4 Phantom impact experiment. In order to determine the force to crush the A320 FE model, the influences of aircraft longitudinal crushing strength on the impact process were analyzed based on the Riera function. Considering the containment decaying effect to aircraft impact velocity, the impact impulse was theoretically calculated, while the influences of the losses of mass and energy were not included. The numerical simulations of A320 aircrafts impacting on simplified NPP containments with different radii were conducted, which could well reproduce the airframe crushing and debris scattering. By comparison of the simulated impact impulses and the calculation values by the Riera function, the coefficients corresponding to different containment radii are derived and a fitting formula is obtained. Finally, an improved Riera function dependent on the dimensionless ratio of nuclear containment radius and aircraft wingspan is proposed.

A series of hard projectile high-speed (500–700 m/s) impact tests on the steel fiber reinforced high strength concrete (SFRHSC) panel with rear steel liner and (or) backfilled sandy soil were conducted. The impact resistance of the above layered composite target as well as the parametric influences were assessed experimentally. It indicates that, within the discussed parameters variation ranges: (i) the rear sandy soil layer enhance the impact resistance of the SFRHSC/steel composite target; (ii) the steel liner also enhance the impact resistance of SFRHSC/sandy layer composite target; (iii) the strengthening effect of the rear sandy soil layer on the impact resistance of bare SFRHSC panel is more influential than the rear steel liner; (iv) Reinforcing steel bars of the concrete panel has no obvious effect on the impact resistance of SFRHSC/steel/sandy soil composite target; (v) Mixing steel fibers can efficiently reduce the damages of the concrete target. An approach for predicting the ballistic limits of SFRHSC/steel and SFRHSC/steel/sandy soil composite targets were proposed and compared with the present test data.

The ultra-high performance steel fiber reinforced concrete (UHP-SFRC) with the corundum coarse aggregate (UHP-CASFRC) was prepared under common curing temperature and pressure procedures. The static tests on UHP-CASFRC were conducted, including the uniaxial compression, direct tensile and four points bending tests. Totally 16 shots of reduce-scaled projectile penetration tests on UHP-CASFRC and 2 comparative shots on HSC targets were conducted. The influences of the strength (hardness), size and volumetric ratio of coarse aggregate, incident velocity of the projectile (510–850 m/s) as well as the repeated strikes on the depth of penetration (DOP), area and volume of the impact crater, as well as the structural integrity and mass loss of the projectile were discussed. By comparisons with the previous conducted basalt aggregated UHP-SFRC (UHP-BASFRC), the superior projectile impact resistance of UHP-CASFRC targets was verified. Within the discussed parametric variation ranges, it derived that: (i) Enlarging the size of the coarse aggregates can help reducing the DOP, impact crater area and volume, the harder coarse aggregate can decreasing the DOP by aggravating the mass abrasions of the projectile. The influences of coarse aggregate hardness on impact crater area and volume mainly depends on its surface roughness; (ii) When the sizes of the coarse aggregates were less than the projectile shank diameter ( d ), the harder coarse aggregates only aggravates the mass abrasions of the projectile, while the structural integrity of projectile could be maintained; (iii) For UHP-CASFRC target, the structural destruction of the projectile occurred when the coarse aggregates sizes increasing larger than d . From a structure protective point of view, the corundum sizes ≥1.5 d is suggested; (iv) The hardness of the coarse aggregate is the most influential factor on the mass abrasion of the projectile, and the previously proposed engineering models for mass abrasions of the ogive-nosed projectile high-speed penetrating into concrete target are further validated.

This paper presents a three-dimensional (3D) mesoscopic model to investigate the responses of closed-cell metallic foams subjected to static and dynamic loadings, especially focusing on the 3D mesoscopic model and the mechanical response. In the first part of this paper, we propose the algorithms to generate the 3D convex polyhedrons modeling the pores with random shapes in closed-cell metallic foams. The 3D mesoscopic model of the foams and the finite element grid are proposed using the ‘take & place’ algorithm and the mapping algorithm. In the second part of this paper, the finite element grid is coupled into the commercial hydrocode LS-DYNA and the ALE analysis approach considering the fluid (the entrapped air) and the structure (the cell-walls) interaction is used. The plastic kinematic model and the linear polynomial equation of state are employed to simulate the cell-walls and the entrapped air, respectively. The responses of closed-cell aluminum foams subjected to static and dynamic compression at high strain rates are simulated by the proposed model and analysis approach. It is demonstrated that the simulated results agree well with test data and the entrapped air plays an important role in the responses when the foams undergo large deformation. Finally, numerical simulations are conducted using the validated approaches, focusing on the effects of mesoscopic configurations (such as the pore size, average density and cell wall strength) on the dynamic responses and the mesoscopic failure patterns. The results show that the collapse and the fracture of the cell walls behave differently under static and high strain rate loadings.

This paper presents a three-dimensional (3D) mesoscopic model of closed-cell aluminum foams. This model is different from the model developed using Voronoi technique. Randomness of pores in shape and distribution is taken into account. The cell-wall thickness varies spatially which is consistent with test observations. Energy analysis approach is presented and validated. Numerical simulations are conducted to investigate the energy absorption capability of the closed-cell aluminum foams under impact loading. Effects of mesoscopic configurations of aluminum foams (cell-wall strength and porosity) on energy absorption capability are investigated numerically. Mesoscopic responses of the cell-walls are discussed to reveal the mechanism of energy absorption capability. It reveals that the energy absorption capability originates from the permanent deformation (plastic strain, collapse and fracture) of cell-walls under impact.

Twenty-five shots of reduce-scaled projectiles perforation test on five configurations of monolithic and segmented RC panels with a rear steel liner were conducted. The impact resistances of layered bare RC and RC/steel composite targets were analyzed quantitatively based on the obtained striking and residual velocities of the projectiles, and the accuracy of the newly developed small-caliber accelerometer in recording the high-amplitude accelerations of the projectile is validated. The main conclusions are: (1) With the same overall thickness and projectile striking velocity, the stacked segmented targets have higher impact resistance than the spaced segmented targets. (2) For the spaced segmented targets with the same total thickness (i) the impact resistance of the monolithic RC plate is better than that of the segmented target, which is not dependent on the impact velocity as well as the rear steel liner is attached or not; (ii) the more the layers of the segmented target, the more inferiority of the segmented target has; (iii) while the number of the layers is fixed, e.g. double layers in the present test, the impact resistance of the segmented target is dependent on the order of the slabs, which is enhanced with the thickness of the later RC plate increasing. (3) An explicit dimensionless expression for predicting the terminal ballistic parameters of the projectile perforating the RC slab was proposed and well validated. (4) The newly proposed equivalent approach for predicting the ballistic limit of the projectile perforating RC/steel composite target was evaluated with the present tests.

The ultra-high performance cement based composites (UHPCC) with the additions of steel fibers and basalt coarse aggregates was prepared under ambient temperature and pressure. In order to apply the UHPCC in the constructions of anti-strike protective structures, the impact resistance of UHPCC was investigated experimentally by conducting the high-speed projectile penetration tests with the broad striking velocities from 510 m/s to 1320 m/s. The rigid and mass abrasive penetration regimes are observed when the projectile striking velocity was lower than 1 km/s and increased up to 1–1.5 km/s, respectively. The experiments validated that UHPCC material has excellent projectile impact resistance, such as reducing the depth of penetration (DOP) and the crater dimensions of the rigid projectile, as well as defeating the structure and deviating the terminal ballistic trajectory of the abrasive projectile. The previously proposed models for rigid penetration depth on fiber reinforced high strength concrete as well as the limit striking velocity causing the structural destruction of mass abrasive projectile are both well validated. The parameters influential analyses further indicate that UHPCC with the compressive strength of 90 MPa and steel fiber mixing ratio of 1.5% is the most efficient and economical choice for protective structure constructions. In details, within the discussed ranges: (i) the projectile impact crater dimensions enlarges with the increase of the compressive strength of the target and the projectile striking kinetic energy, and which was reduced with the increase of fiber mixing fraction and the mixed coarse aggregate. The influential degree of mixing fibers on reducing the cratering dimensions is much greater than which of compressive strength on enlarging the cratering dimensions; (ii) both of the compressive strength, the fiber mixing fraction as well as coarse aggregates can help decreasing the DOP of the projectile so as to enhance the impact resistance of the target, while the contribution of fibers is very limited for the relatively low addition ratio (⩽3%). The DOP of the projectiles are no longer decreasing obviously when the compressive strength of the target is larger than nearly 90 MPa.