Hard Projectile Impact Research Articles

Reinforced concrete structures under hard projectile impact: penetration and perforation resistance

AbstractReinforced concrete (RC) structures are mainly designed to withstand both static and dynamic loads. However, due to the highly nonlinear behavior of RC structures subjected to extreme dynamic loads, these structures have a very complex damage behavior under dynamic impact loading. In fact, current existing methods for damage‐simulation and prediction are generally based on either empirical data, simplified mechanical approaches or complex numerical simulations mainly using the finite element method. In this regard, empirical and semi‐empirical models can be considered to calculate the load‐bearing capacity in a simplified way with only a few input parameters. Hence, using current experimental test data, this paper aims to analyze and assess existing empirical and semi‐analytical approaches that are established in standards and guidelines. Accordingly, a functional relationship in terms of an impact factor is found. Based on the obtained results, different approaches are also developed to describe the resistance to projectile penetration of RC structures as well as the force interaction between projectile and RC structures.

A performance-based ballistic design framework for RC panels and a probabilistic model for crater quantification

Ballistic design is crucial for widely utilised concrete structures in today’s unpredictable world. In the past, extensive experimental and numerical studies have investigated concrete panels, resulting in design guidelines and empirical formulations for local damage parameters. However, with the advent of performance-based design, notably in seismic design, the ballistic design of concrete structures lacks a comprehensive design philosophy. Additionally, deterministic empirical formulations for local damage parameters, particularly in the case of reinforced concrete (RC) panels’ crater formation, necessitate a probabilistic treatment. Consequently, this paper addresses the need for a well-defined ballistic design philosophy for concrete structures and introduces a probabilistic approach for crater quantification. Firstly, a novel multi-level and multi-parameter performance-based design framework for RC panels is proposed, centred on damage states, namely depth of penetration and crater area. This framework establishes an innovative design philosophy featuring four damage levels for each state. Secondly, using dimensionless explanatory functions, a Bayesian inference model is developed to estimate the crater diameter in RC panels under hard projectile impact, accounting for the associated uncertainties. LS-Dyna is used for numerical modelling of RC panels and rigid projectiles. The numerical models are validated with the experimental data and are utilised to develop the probabilistic model. This study reveals the profound influence of projectile and concrete properties in addition to the incidence angle of the projectile on crater formation. The developed probabilistic model is validated with experimental results demonstrating its reliability and accuracy. Consequently, a reliable design formula for estimating crater diameter for RC panels under hard projectile impact is proposed in addition to the novel ballistic design framework.

Constitutive model for fibre reinforced composites with progressive damage based on the spectral decomposition of material stiffness tensor

Complex nature of the fibre reinforced composites, their non-homogeneity and anisotropy make their modelling a challenging task. Although the linear – elastic behaviour of the composites is well understood, there is still a significant uncertainty regarding prediction of damage initiation, damage evolution and material failure especially for a general loading case characterised with triaxial state of stress or strain. Consequently, simplifying assumptions are often unavoidable in development of constitutive models capable of accurately predicting damage. The approach used in this work uses decomposition of the strain energy based on spectral decomposition of the material stiffness tensor and an assumption that each strain energy component represent free energy for a characteristic deformation mode. The criteria for damage initiation are based on an assumption that the damage corresponding to a deformation mode is triggered when the strain energy for that mode exceeds a specified critical limit. In the proposed model the deformation modes are not interacting at continuum scale due to orthogonality of the eigenvectors, i.e. the stiffness tensor symmetry. Damage and its evolution are modelled by reduction of the principal material stiffness based on the effective stress concept and the hypothesis of strain energy equivalence. The constitutive model was implemented into Lawrence Livermore National Laboratory (LLNL) Dyna3d explicit hydrocode and coupled with a vector shock Equation of State. The modelling approach was verified and validated in a series of single element tests, plate impact test and high velocity impact of hard projectile impact on an aerospace grade carbon fibre reinforced plastic. The model accurately predicted material response to impact loading including the test cases characterised by presence of shock waves, e.g. the plate impact test. It was also demonstrated that the model was capable of predicting damage and delamination development in the simulation of the high velocity impact tests, where the numerical results were within 5% of the post impact experimental measurements.

Analytical Model Formulation of Steel Plate Reinforced Concrete Walls against Hard Projectile Impact

Steel plate reinforced concrete (SC) walls can effectively resist projectile impact by preventing the rear concrete fragments flying away, thus attracting much attention in defence technology. This work numerically and analytically investigated the hard projectile perforation of steel plate reinforced concrete walls. Impact resistance theories, including cavity expansion analysis as well as the petaling theory of thin steel plates were used to describe the cratering, tunneling and plugging phases of SC walls perforation. Numerical modeling of SC walls perforation was performed to estimate projectile residual velocity and target destructive form, which were validated against the test results. An analytical model for SC wall perforation was established to describe the penetration resistance featuring five stages, i.e., cratering, tunneling and plugging, petaling with plugging and solely petaling. Analytical model predictions matched numerical results well with respect to projectile deceleration evolution as well as residual velocity. From a structural absorbed energy perspective, the effect of front concrete panel and rear steel plate thickness combinations was also studied and analyzed. Finally, equivalent concrete slab thickness was derived with respect to the ballistic limit of SC walls, which may be helpful in the design of a protective strategy.

Comparative study on performance of UHTCC and RPC thick panels under hard projectile impact loading

This paper presents a comparative study on the perforation resistance of thick panels made of the reactive powder concrete (RPC) and the ultra high toughness cementitious composites (UHTCC). Damage patterns of the target were measured, including the diameter and depth of the cratering and scabbing on the front and rear surfaces. Residual velocities of the projectiles were determined by a high speed camera. The test results showed 46 MPa UHTCC has superior resistance to the tensile damage induced cratering and scabbing while its penetration resistance is comparable to NC with a lower compressive strength (30 MPa). The 123 MPa RPC exhibits much higher penetration resistance than UHTCC and NC, and has improved performance over NC in resisting tensile damage. Besides, based on the framework of the Forrestal formula, a unified semi-analytical model is proposed which can predict the penetration and perforation ballistic parameters of thick concrete panel under projectile impact. Compared to the experimental observations, the proposed model predicts the residual velocity and penetration depth of this test with better results than existing models. Finally, the new model is applied to the available perforation tests of thick concrete panels, and its error used for relatively thin concrete panel is analyzed.

Enhancement of engineering models for simulation of soft, and hard projectile impact on reinforced concrete structures

Protective Reinforced Concrete (RC) barrier walls of nuclear or industrial facilities are required to withstand accidental or intentional missile impact. The missiles (projectiles) can be classified as hard, semi-hard or soft. In particular, an airplane crash on a reinforced concrete structure causes local and global damage to the structure. Local damage mechanisms are usually associated with the impact of hard aircraft components such as engine shafts and wing boxes. In the event of a hard impact, the contact actions and target reactions are strongly coupled and therefore the calculation of capacity and damage effects is very sophisticated.There are various analysis methods for modelling both, hard and soft impacts. In this regard, empirical and semi-empirical models can be considered to calculate the load-bearing capacity in a simplified way with a few input parameters. However, validated numerical Finite Element (FE) simulation models allow further investigation on damage mechanism as well as detailed evaluation of stresses and strains in concrete and reinforcement.Hence, this paper investigates the efficiency of the existing analytical approaches as well as numerical simulation methods in predicting the load-bearing capacity of rc structures under hard and soft impact loads. Moreover, a novel simplified mechanical analytical method is proposed concerning hard impact loads. The mechanical principles are based on a nonlinear two degree of freedom (TDOF) system by Schlüter (Schlüter, 1987), which was extended for applications on hard impact scenarios considering the interaction between the impacting projectile and the rc target as well as penetration process of the projectile. FE-simulations and experimental test results of recent and ongoing research projects are presented and have been used for validation purposes and investigations.

Effect of Reinforcing Steel on the Impact Resistance of Reinforced Concrete Panel Subjected to Hard-Projectile Impact

Experimental and numerical studies were conducted to investigate the effect of reinforcing steel on the impact resistance of reinforced concrete structures and to reveal its mechanism. Hard-projectile impact tests using a single-stage gas gun were performed with reinforced concrete panels to simulate a nuclear power plant structure. Parametric analysis was conducted with a numerical model that applied a finite element method coupled with smoothed particle hydrodynamics using the following four variables: the impact velocity of the projectile as well as yield strength, spacing and diameter of the reinforcing steel. The experimental and numerical analysis results indicated that the impact resistance was significantly affected by the spacing of the reinforcing steel, but not by the yield strength or the diameter of the reinforcing steel. Narrower rebar spacing improved the impact resistance due to the enhanced confining and fragment trapping effects.

Experimental and numerical studies on the impact resistance of large-scale liquefied natural gas (LNG) storage outer tank against the accidental missile

Regarding the disastrous consequences when the dome or cylindric wall of Liquefied Natural Gas (LNG) was damaged, the large-scale LNG storage tank should be designed to resist the potential impact loadings, e.g., turbine and wind-borne missiles. This paper aims to study the impact resistance of large-scale LNG storage outer tank subjected to the accidental low-velocity and large weight missile experimentally and numerically. Firstly, the reinforced concrete/steel liner (RC/steel) composite targets designed according to the dome of LNG storage tank were fabricated. Fifteen free dropping tests of rigid impactor on the RC/steel targets were conducted, in which the mass of the impactor were 500 kg, 800 kg and 1100 kg, and the corresponding impacting velocities were ranged from 14 m/s to 26.19 m/s, respectively. The local damage and failure modes of RC/steel target panels under large caliber hard projectile impact are assessed experimentally. Then, the commercial finite element (FE) program LS-DYNA was utilized to perform the corresponding numerical simulations, the numerical algorithm, constitutive models and the corresponding parameters are validated by comparing with the test data. Finally, the impact resistance of the prototype of Chinese Dalian large LNG storage outer tank subjected to the accidental impact of missiles specified by British standard BS 7777 and United States regulatory guide U.S. 1.76 are evaluated numerically. The present work and conclusions can provide helpful references for the design and impact resistance evaluation of large-scale LNG storage tank subjected to the accidental missile.

An investigation of ballistic response of reinforced and sandwich concrete panels using computational techniques

Structural performance of nuclear containment structures and power plant facilities is of critical importance for public safety. The performance of concrete in a high-speed hard projectile impact is a complex problem due to a combination of multiple failure modes including brittle tensile fracture, crushing, and spalling. In this study, reinforced concrete (RC) and steel-concrete-steel sandwich (SCSS) panels are investigated under high-speed hard projectile impact. Two modeling techniques, smoothed particle hydrodynamics (SPH) and conventional finite element (FE) analysis with element erosion are used. Penetration depth and global deformation are compared between doubly RC and SCSS panels in order to identify the advantages of the presence of steel plates over the reinforcement layers. A parametric analysis of the front and rear plate thicknesses of the SCSS configuration showed that the SCSS panel with a thick front plate has the best performance in controlling the hard projectile. While a thick rear plate is effective in the case of a large and soft projectile as the plate reduces the rear deformation. The effects of the impact angle and impact velocity are also considered. It was observed that the impact angle for the flat nose missile is critical and the front steel plate is effective in minimizing penetration depth.

Improving the resistance of concrete panels to hard projectile impact

In this article, the response of nine plain concrete panels to an impact of hard projectiles was examined in an experimental study. The tests were planned with an aim to observe the influence of compressive strength on the performance of concrete under impact loading. Concrete panels with compressive strengths within the range of 26 to 92 MPa subjected to impact by 23 mm hard projectile at velocities within the range of 270 to 348 m/s were studied. Also, using a glass fiber reinforced polymer sheet, as a liner on the rear face of the plain concrete panel, to strengthen the panel was examined. The experimental results indicate that strengthening concrete panel with a rear glass fiber reinforced polymer sheet showed more satisfactory performance under the impact load than increasing compressive strength of concrete. Also, the use of glass fiber reinforced polymer sheets as rear liners in addition to increasing the concrete strength showed superior performance of concrete panels against impact; it is recommended to be used in protective structures.

Improving the impact resistance of concrete panels by glass fiber reinforced polymer sheets

In this article, the response of 12 plain concrete specimens to an impact of hard projectiles was examined in an experimental study. The tests were planned with an aim to observe the influence of using glass fiber reinforced polymer sheets to strengthen plain concrete panels on the performance of concrete under this type of loading. The main findings show that strengthening plain concrete panels with glass fiber reinforced polymer sheets showed satisfactory performance under the impact load; the glass fiber reinforced polymer sheets can be used for strengthening or upgrading concrete structures to improve their resistance against impact. Also, the location of the glass fiber reinforced polymer sheet affects the front and rear face craters.

Effect of CFRP strengthening on the response of RC slabs to hard projectile impact

In this paper impact response of CFRP-strengthened RC panels under the impact of non-deformable projectiles has been presented. The control and CFRP-strengthened RC slab panels were tested under the strike of hemispherical nosed steel projectiles at varying impact velocities. The response of these panels was investigated experimentally as well as numerically. The damage of the slab panels was measured in terms of the penetration depth, formation of cracks, spalling and scabbing areas and fracture of CFRP sheet. This study presents a practical and efficient numerical method for analyzing the impact response of CFRP-strengthened RC structures using LS-DYNA. The CFRP strengthening was found to increase the ballistic limit velocity by 18%, perforation energy of RC slabs by 56.7%, reduce the front crater damage and contains the flying of concrete fragments from the rear face. The maximum impact force occurs at almost same penetration depth for the control and CFRP-strengthened slabs but the restraint provided by CFRP increased the penetration depth by about 1/19.3 of the thickness of slab.

Reliability of double-wall containment against the impact of hard projectiles

Effectiveness of single or double-wall containment structures against a possible strike of projectiles, missiles or airplanes is well researched. However, how the uncertainties involved in the various design parameters influence the reliability of the containment is not very well known. In a double-wall containment structure, as name implies, there are two walls – an outer thick reinforced concrete (RC) wall and an inner thin steel shell/wall. In the present study, a simple probabilistic procedure based on Monte Carlo simulation technique is presented to study the reliability of double-wall containment structures against the impact of external hard projectiles on outer RC wall for varying impact velocities. In order to illustrate the proposed methodology, an idealized double-wall containment structure and a hard projectile were chosen. The probability of failure and the reliability indices of the selected double-wall containment structure were obtained for different striking velocities of the projectile and safety of the containment was correlated with the ballistic limit of the outer RC wall. The results of the study show that the double-wall containment is “safe enough” against the impact of the selected projectile if the projectile nominal velocity is less than 65% of the containment outer wall's nominal ballistic limit (VBL). Results also show that under the given uncertainties, if the nominal impact velocity is less than 65% of the nominal ballistic limit of the outer RC wall (i.e. 0.65VBL), failure probability of the containment is almost zero. However, when impact velocity is more than 0.90VBL, failure probability of the double-wall containment is quite high. It was also observed that a little change in the impact velocity over 0.90VBL may cause a phenomenal change in the containment reliability due to substantial change in the residual kinetic energy of the projectile. A number of sensitivity studies have also been carried out to obtain the results of practical interest.

Effect of reinforcement on the response of concrete panels to impact of hard projectiles

The impact of a hard projectile on a concrete target is a complex incident which cannot be described accurately without giving consideration to the effects of the different variables involved and to the associated physical phenomena. Among these variables are the reinforcement details in the concrete target. In this paper the response of 26 concrete specimens, with 500 × 500 × 100 mm3 dimensions, to an impact of 23 mm, 0.175 kg hard projectiles was examined in an experimental study. The tests were planned with an aim to observe the influence of the ratio and type of reinforcement (embedded rebar mesh or steel plate lining) on the performance of concrete under this type of loading. The variants that were examined were the location of reinforcement mesh and steel plate lining (front, rear, and both front and rear). The main findings show that the location of the reinforcement mesh affects the front and rear face craters. Also lining concrete target with front and rear steel plates has positive effect on the perforation resistance.

Normal impact of hard projectiles on concrete targets

AbstractThis research study involves obtaining an analytical model for the perforation of unreinforced concrete targets by a hemispherical hard projectile. Dynamic cavity expansion theory and the reflection of compressive waves from the end of the concrete targets are used for developing the analytical model. The effect of the friction coefficient is also investigated in the analysis. Numerical modelling of the problem has been performed in LS‐DYNA code for validating the analytical results. Johnson‐Holmquist concrete and rigid material models have been employed for the concrete and the projectile respectively. The impact velocity range considered in this work is between 250 and 850 m/s. No projectile erosion is considered in this range. The analytical results have been compared with numerical results and show good agreement with numerical simulations.

Response of hybrid-fiber reinforced concrete slabs to hard projectile impact

In the present study, the effectiveness of hybrid-fibers (a combination of steel and plastic fibers) in improving the impact resistance of slabs was studied through a detailed experimental program. A total of 54 hybrid-fiber reinforced slabs were cast in the two groups; each group containing 27 slabs. The specimens of the first group were cast using normal strength concrete, whereas specimens of second group were cast using high strength concrete. All the slabs were 600 × 600 × 90 mm and contained different proportions of steel and plastic fibers. Out of a total number of 54 slabs, three slabs in each group were used as control specimens i.e. without fibers. The impact penetration tests were carried out using an air-gun system. The projectiles were made of hardened steel and were bi-conic in shape. Failures of the specimens were observed and size of the front and the rear face craters and the penetration depths were measured. The test results showed that the hybrid-fibers in the concrete lead to smaller crater volumes and reduce the spalling and scabbing damage. The hybrid-fibers arrest the crack development and thus minimize the size of the damaged area. The penetration depth and perforation thickness were predicted by modifying the impact function of NDRC equation to incorporate the effects of hybrid-fibers. The ballistic limit was also predicted. A simple formulation was then proposed for the prediction of the ejected concrete mass from the front and the rear faces of the specimens. Predictions matched well with the experimental observations.

Ballistic impact on bi-layer alumina/aluminium armor: A semi-analytical approach

This paper presents a semi-analytical approach on the performance of ceramic/metal armor under ballistic impact. Numerical simulations for alumina/aluminum armor impacted by 20 mm APDS in AUTODYN were carried out and verified against the experimental data. Comprehensive numerical simulations were performed using the verified numerical model material parameters providing corroborative data for ensuing discussions. A semi-analytical model relating projectile residual velocity, impact velocity and armor ballistic limit velocity (BLV) is presented for impact of hard projectile against ceramic/metal armor. It is shown that the projectile residual velocity and BLV satisfy the replica scaling laws. Based on the replica scaling laws of projectile residual velocity and BLV, an empirical equation for BLV is obtained and used for armor optimization applications giving reasonable results similar to experiments available in the literature.

Analytical Model for Critical Impact Energy of Spalling and Penetration in Concrete Wall

Penetration is the basic element of designing protective concrete structure against the local impact of hard projectile. Conventional, un-conventional, and sensitive structures should have to be designed as self-protective structures in order to resist natural disaster, consciously engendered unpleasant incidents, or/and against accidently occur incidents in nuclear plants, local industries etc.. When hard projectile collides with concrete wall, it is the critical impact energy of the projectile that deforms concrete wall. Critical impact energy is the dominant cause of penetration in concrete structures. Therefore, it is vital to study critical impact energy that causes penetration. An analytical model is developed to predict the required critical impact energy for spalling and tunneling and maximum penetration without rear effects in concrete walls when it is impacted with hard projectile. The newly developed analytical model is examined for CRH =2.0, 3.0. It was found that the predicted results from analytical model are in close relation with experimental data with less than (8%) and (17%) error in case of CRH =2.0 and 3.0. Furthermore, Chen and Li nose shape factor is modified as ( N i ), with introduction of empirical frictional factor ( N f ). It was found that the predicted results from analytical model with proposed nose shape ( N i ) are in close relation with experimental data in all cases as compared to predicted results with traditional Li and Chen nose shape ( N * ). In general, the analytical model generates encouraging prediction which is consistent and follows a general trend of experimental results. Therefore, it is suggested that the proposed analytical model is conservative.

Analytical Model for Critical Impact Energy of Spalling and Penetration in Concrete Wall

Penetration is the basic element of designing protective concrete structure against the local impact of hard projectile. Conventional, un-conventional, and sensitive structures should have to be designed as self-protective structures in order to resist natural disaster, consciously engendered unpleasant incidents, or/and against accidently occur incidents in nuclear plants, local industries etc.. When hard projectile collides with concrete wall, it is the critical impact energy of the projectile that deforms concrete wall. Critical impact energy is the dominant cause of penetration in concrete structures. Therefore, it is vital to study critical impact energy that causes penetration. An analytical model is developed to predict the required critical impact energy for spalling and tunneling and maximum penetration without rear effects in concrete walls when it is impacted with hard projectile. The newly developed analytical model is examined for CRH =2.0, 3.0. It was found that the predicted results from analytical model are in close relation with experimental data with less than (8%) and (17%) error in case of CRH =2.0 and 3.0. Furthermore, Chen and Li nose shape factor is modified as ( N i ), with introduction of empirical frictional factor ( N f ). It was found that the predicted results from analytical model with proposed nose shape ( N i ) are in close relation with experimental data in all cases as compared to predicted results with traditional Li and Chen nose shape ( N * ). In general, the analytical model generates encouraging prediction which is consistent and follows a general trend of experimental results. Therefore, it is suggested that the proposed analytical model is conservative.

Hard Missile Impact on Prestressed Shear Reinforced Slab

The protective concrete walls of nuclear power plants must withstand accidental or intentional missile impact, and structural systems and solutions are being developed in building frameworks and detailed levels requiring sophisticated tools for different design phases such as detailing shear reinforcement. Numerical methods, for example, have been developed and used for predicting prestressed shear reinforced concrete structures response subjected to hard projectile impact. The structural behavior of prestressed impact-loaded walls is predicted analytically and by using nonlinear FE models. Analysis predicts damage mechanisms such as crater formation, penetration, shear cone formation, and perforation. To produce experimental data required to verify the accuracy of numerical models, an experimental setup has been developed at the Technical Research Center of Finland (VTT) for intermediate-scale impact testing enabling force-plate testing with soft missiles and concrete slab impact testing.