Semi-infinite Concrete Targets Research Articles

Experimental and theoretical study on cavitation of concrete targets penetrated by hypervelocity long rod projectiles

The cavitation phenomenon can seriously decrease the strike performance of military weapons. As military terminal-ballistic activities have turned to hypervelocity attacks, the cavitation effect existing in the hypervelocity penetration deserves more attention. In terms of long-rod hypervelocity penetration into concretes, this study presents an analytical cavity model for the prediction of the cavity diameter based on the two-stage cavitation mechanism and the u-v relationship. The two-stage mechanism involving mushrooming and radial momentum expansion is used to describe the cavitation modes and the penetration parameters for the projectiles used in the analytical model are determined by numerical simulations empirically. Besides, the three modes including rigidity, deformation and erosion are introduced into the cavity model to elucidate the projectile state. Moreover, the hypervelocity impact experiments on the long rods into semi-infinite concrete targets at velocities of 2117 ∼ 3086 m/s are carried out to observe the cavitation effect of concrete targets and for further validating the model through comparing with the experimental cavity profiles, where the cavity profile is quantified with silica gel, and the cavity diameter is found to be more than five times the projectile diameter. The cavitation effect is observed significantly and quantified from the experiment results. The cavity model is compared with the experimental cavity profiles, showing that the model has good applicability.

Flow field analysis of long rod hypervelocity penetration into semi-infinite concrete target

An ovoid of Rankine was used to describe the flow field shape, and a flow field analysis model was constructed to depict the penetration process. The depth of penetration, tunnel radius, change in the long rod length, and penetration velocity was calculated using this model. The calculation results were in good agreement with experimental data from previous studies. The influence of long rod material parameters on penetration was also analyzed. The following results were obtained: the depth of penetration increased slowly with increasing impact velocity at hypervelocity penetration, the erosion rate of the long rod was constant during the penetration process, and the length of the long rod was the most sensitive parameter affecting the depth of penetration, and the hole radius and long rod diameter had an approximately linear relationship and both increased with rod density.

Determination of critical ricochet conditions for oblique impact of ogive-nosed projectiles on concrete targets using semi-empirical model

This paper presents a simple and efficient semi-empirical model for predicting the dynamic behaviors of rigid ogive-nosed projectiles after obliquely impacting semi-infinite concrete targets. We consider the normal stress acting on the projectile surface as a result of the target resistance. We also reflect the decrease in normal stress caused by crater formation and the presence of the free surface on the target. The normal stress is formulated as a function of the projectile geometry and the properties of the target material. To verify the proposed semi-empirical model, we establish computational frameworks combining the finite element method and smoothed particle hydrodynamics. These frameworks are confirmed to provide results consistent with the experimental data for the normal impact of projectiles on concrete targets. By comparing the results obtained from the semi-empirical model with the reference results obtained from the computational frameworks, we demonstrate that the semi-empirical model can successfully predict the penetration or ricochet of projectiles following oblique impact. Furthermore, considering the nose sharpness, slenderness, impact velocity, and oblique incidence angle of the projectiles as key parameters, we investigate their effects on the dynamic behaviors of projectiles. The penetration capabilities of projectiles increase with sharper and slenderer geometry, higher impact velocity, and lower incidence angle. In particular, considering various combinations of these parameters, we identify the critical conditions for the incidence angle and impact velocity that lead to the ricochets of projectiles. The minimum incidence angle, at which ricochets occur, increases in proportion to the nose sharpness, slenderness, and impact velocity. The maximum impact velocity, up to which ricochets occur, decreases as the nose sharpness and slenderness increase and the incidence angle decreases.

Study on the Equivalence of Penetration Overloading for Projectile-Borne Components in Nonproportional Penetrators

The reliability assessment of the projectile-borne components in a high-speed penetrator is an important issue in the penetration field. In this study, a scaling model embedded with a deceleration measurement device was used to investigate the overloading situation due to the high cost of the prototype test. The projectile could be scaled, while the deceleration measurement device needs to maintain full scale. Thus, a nonproportional scaling design is proposed to represent the rigid-body deceleration of the prototype projectile. This study, considering the mass of the deceleration measurement device, lays out the design criteria of the scaling model and carries out rigid-body deceleration similarity verification tests of the prototype and the scaling model. In addition, the rigid-body deceleration similarity was examined through model predictions and numerical simulation. These results show that the rigid-body deceleration of the nonproportional scaling model is generally in agreement with that of the prototype for penetrating the semi-infinite concrete target. The deviations of rigid-body deceleration magnitude and duration are 6.76% and −12.1%, respectively. This makes it reasonable and feasible to investigate the overloading situation of prototype projectile through a nonproportional scaling model.

Study on the penetration of elliptical cross-section projectiles into concrete targets: theory and experiment

To better understand the penetration mechanism of the elliptical cross-section projectile (ECSP) into semi-infinite concrete target, penetration experiments using three types of ECSPs with different shape ratios (1, 1.25 and 1.61) and with striking velocities ranged from 550 m/s to 1050 m/s were conducted. Penetration depths, penetration trajectory and mass erosion rates of the projectile were obtained after the experiments. The experiment results show that the penetration performance and ballistic stability of the ECSP are equivalent to those of the circular cross-section projectile (CCSP). Based on the theory of complex variable function and conformal transformation, a semi-analytical model which can calculate the cavity boundary stress distribution of elliptical section cavity controlled by the displacement boundary condition was established and the model was validated by comparing the model degenerate solution with Kirsch problem results. Theoretical calculation results show that the radial stress of elliptical section cavity increases progressively from the minor axis to the major axis. In addition, a formula combining with the semi-analytical theoretical model and the local interaction theory was developed. The predicted penetration depths were compared with 30 groups of experiment data with different projectile parameters and striking velocities and coincide quite well with the corresponding experimental data. Finally, the influence of shape ratio and caliber-radius-head (CRH) on the penetration performance of projectile and the application prospect of ECSPs on hypersonic weapon platform were studied.

Research on the Shock Response Characteristics of a Threaded Connection Using the Thin-Layer Element Method

Nonlinear factors such as the contact stiffness and friction damping at the threaded interface of a projectile–fuse system significantly affect the dynamic response characteristics. To obtain the dynamic response of the fuse body accurately during penetration, it is necessary to characterize these nonlinear factors reasonably. Because the existing structural dynamics software cannot effectively deal with nonlinear factors, the thin-layer element method was used to represent the nonlinear factors in this study. By combining the thread elastic model with thin-layer element principles, an effective method for determining the material parameters of the thin-layer element was established theoretically, which provided a different method of determining material parameters, not just relying on experiments. The accuracy of the material parameters was verified based on modal experiments with threaded tubes having different specifications. The errors were within 5%, indicating the reliability of the theoretical determination method for the material parameters. In addition, projectile penetration into a semi-infinite concrete target was tested to verify the accuracy of the thin-layer element modeling. Compared with the ‘TIED’ constraint method, the resonant frequency obtained with the thin-layer element method was in better agreement with that of the experimental data. The maximum error decreased from 15.7 to 7.8%, indicating that the thin-layer element method could accurately represent the nonlinear factors. Thus, this study serves as a reference for accurately evaluating the dynamic response of the fuse body of a penetrator.

Numerical study on the resistance of rigid projectiles penetrating into semi-infinite concrete targets

A study on the resistance of rigid projectiles penetrating into semi-infinite concrete targets is performed in this paper. Experimental data are analyzed to examine the penetration resistance during various stages of the penetration process. A numerical tool using AUTODYN hydrocode is applied in the study. The numerical results on both deceleration-time history and depth of penetration of projectiles are in good agreement with experimental data, which demonstrate the feasibility of the numerical model in these conditions. Based on the numerical model with a two-staged pre-drilled hole, the rigid projectile penetration in tunneling stage is studied for concrete targets with different strengths in a wide range of impact velocities. The results show that the penetration in tunnel stage can be divided into two different cases in terms of initial impact velocity. In the first case, when the impact velocity is approximately less than 600 m/s, the deceleration depends on initial impact velocity. In the second case, when the impact velocity is greater than 600 m/s, the effect of target inertia becomes apparent, which agrees with commonly used concrete penetration resistance equations based on cavity expansion model. A two-staged pre-drilled hole model was developed and the results show that the depth of entrance stage tends to decrease with the increase of impact velocity. The influence of the inertial term at low velocity range (approximately close to 600 m/s) is inconspicuous. With further increase of the penetration velocity, the effect of the target inertia becomes apparent as proposed by Forrestal. The effect of mass abrasion of projectiles, entrance phase and strain effect of concrete materials on the tendency of deceleration was clarified.

Failure analysis of semi-infinite concrete targets subjected to tubular projectiles impact

Improving the penetration efficiency of missiles into concrete is a practical research topic. In this paper, a tubular projectile was designed to enhance penetration diameter on concrete targets. To validate numerical simulation methods, an experiment of an ogive-nosed projectile penetrating a semi-infinite concrete target was reproduced by numerical simulation. Based on the validated numerical model, the penetration progress of a tubular projectile into a semi-infinite concrete target was analyzed. By assessing the penetration tunnel diameter and depth, the effects of key parameters, i.e., the wall thickness (15.0, 30.0, 60.0, 90.0, 120.0 mm) and velocity (400.0, 600.0, 800.0, 1000.0, 1200.0, 1400.0 m/s) of tubular projectile on penetrating concrete targets have been investigated in detail. Furthermore, the penetration performances of flat-nosed projectiles and tubular projectiles on concrete targets with the same mass were compared. The results indicate that with the increase in the wall thickness and velocity of the tubular projectiles, the penetration depth of the projectiles into the concrete target increases gradually, and the increase in the diameter of the tunnel is not obvious. In the case of the wall thickness of the tubular projectile which is greater than or equal to 30.0 mm, the concrete core, near the head of the tubular projectile, is completely fractured and separated from the concrete target. When the flat-nosed projectiles have the same mass and length with tubular projectiles, the diameter of the tunnel caused by the tubular projectile on the concrete targets is always much larger than that caused by the flat-nosed projectiles. The difference of them can be 60.5%. In the condition that the flat-nosed projectiles have the same mass and diameter with tubular projectiles, the depth of the tunnels caused by tubular projectiles in the concrete targets is always much larger than that caused by flat-nosed projectiles. The difference of them can be 95.6%.

Hypervelocity penetration of concrete targets with long-rod steel projectiles: experimental and theoretical analysis

Hypervelocity penetration experiments were performed on semi-infinite concrete targets with 7 mm-diameter 40CrNiMo steel long-rod projectiles at impact velocities ranging from 2117 m/s to 3086 m/s by using a two-stage combustion light-gas gun. After the experiments, the crater dimensions and penetration depth were carefully measured, also the residual projectiles were recovered. The depth of penetration was found to be greater than the hydrodynamic limit penetration depth. Numerical simulation was conducted to analyze the penetration process, and combined with the experimental results, it was obtained that the head of the long-rod projectile eroded and deformed into a hemisphere during hypervelocity penetration. According to the experimental and numerical simulation results, the penetration model of long-rod projectiles penetrating concrete targets at hypervelocity was constructed based on the Alekseevskii-Tate model. The penetration model was compared with the experimental depths of penetration, showing that the model had good applicability.

Hypervelocity Impact Cratering on Semi-Infinite Concrete Targets of Projectiles with Different Length to Diameter Ratios

Impact cratering experiments were performed on semi-infinite concrete targets with 7 mm-diameter 40CrNiMo steel long-rod projectiles at impact velocities ranging from 2117 m/s to 3086 m/s by using a two-stage combustion light-gas gun. After the impact experiments, the crater diameter and depth as well as the crater volume were carefully measured. The concrete fragments were collected from the target chamber and the fragment mass was measured. The size of the crater (including the volume, diameter, and depth) and the fragment mass increased with increasing impact velocities, while the fragment distributions at different impact velocities were almost the same. Scaling laws for the crater volume impacted by the rod-shaped projectile were discussed and an empirical formula of crater volume was determined by the experimental data from the literature. Through the verification of the present experimental results, the predictive ability of the empirical formula proved to be reliable. Scaling laws for the size distribution of concrete fragments were also discussed. The normalized fragment mass distribution was proportional to the impact velocity raised to the power 1.5.

A rigid elliptical cross-sectional projectile with different geometrical characteristics penetration into concrete target

Elliptical cross-sectional projectiles have recently attracted attention because they fit the flattened shape of earth-penetrating weapons. This study aims to investigate a rigid elliptical cross-sectional projectile with different geometrical characteristics penetration into the semi-infinite concrete targets by implementing a theoretical method. The general geometric models of four types of elliptical cross-sectional projectiles are introduced; closed-form penetration equations are then derived based on the dynamic cavity-expansion theory. Furthermore, the present models are validated by comparing the predicted penetration depths with the predictions obtained using the semi-empirical formulae and test data; the maximum deviation from the test data is 15.8%. In addition, the deceleration, velocity, and displacement of the projectiles during the penetration process are obtained based on the present models, and the penetration performance of the four types of elliptical cross-sectional projectiles is discussed by comparing the penetration depths. The conical-nose elliptical cross-sectional projectile exhibits the best penetration performance than the other three types if the nose length is sufficiently large, and the ogive-nose elliptical cross-sectional projectile gradually exhibits its penetration performance advantage with the increase in the nose length.

Dynamic spherical cavity expansion analysis of concrete/rock based on Hoek-Brown criterion

Cavity expansion theory has been widely applied to predict the penetration depth of projectiles into geological materials, in which the yield criterion and the constitutive model are combined to describe the shear and compaction of the material, separately. For a precise description of the material behaviors in plastic for geological materials with varied compressive strength, in this present manuscript, the Hoek-Brown yield criterion and the Dilatant-Kinematic equation were introduced into the plastic region. A response region called elastic-cracking-dilatant-compaction region for concrete and rock was established. Then the effects of various parameters, including brittleness coefficient, material integrity coefficient and dilatant coefficient, on the relationship between cavity pressure and normal expansion velocity were discussed. Finally, a penetration depth formula of rigid projectiles into semi-infinite concrete and rock targets was established. It showed that, compared with the classical Forrestal model, the proposed model had a well-being as well as higher accuracy prediction of the penetration depth of concrete and rock materials with various strengths.

Experimental investigation on the cellular steel-tube-confined concrete targets against projectile impact

Steel-tube-confined concrete (STCC) targets show better anti-penetration performance than semi-infinite concrete targets as the steel tube imposes constraint on the in-filled concrete to enhance its strength and toughness. Cellular structural system for in-plane and multi-layer overlay extension is an effective way to promote the application of STCC targets to practical protective structures. In this paper, penetration tests of cellular STCC targets (single-layer and double-layer 7-cell hexagonal STCC targets) impacted by 12.7 mm Armor Piercing Projectile (APP) were conducted, and side length and thickness of steel tube, steel ratio, impact point and velocity, and repeated impacts were considered. Moreover, single-cell STCC targets and semi-infinite concrete targets were also designed and tested for comparison with the cellular STCC targets. The typical damage modes and parameters of the tested cellular STCC targets including the range, depth and volume of funneled crater and depth of penetration (DOP), were obtained and discussed. It is shown that the 7-cell hexagonal STCC targets show improved anti-penetration performance in comparison to the single-cell STCC targets under the same conditions; the anti-penetration performance of the double-layer 7-cell hexagonal STCC targets was weakened due to the free surfaces between the layers; the side length and thickness of steel tube, steel ratio and impact velocity have significant influence on the DOP of the 7-cell hexagonal STCC targets; optimizing the side length and thickness of steel tube could greatly improve the anti-penetration performance of the cellular STCC protective structures. Moreover, the 7-cell hexagonal STCC targets also show excellent anti-penetration performance under the repeated impacts of 12.7 mm APP.

On the penetration of semi-infinite concrete targets by ogival-nosed projectiles at different velocities

Concrete has been widely used to construct protective structures in both civil engineering and defense installations which may be subjected to impact by projectiles at different velocities. In this paper, a theoretical study is presented on the penetration of a semi-infinite concrete target by an ogival-nosed projectile at different velocities within a unified framework. Depending upon impact velocity V0, the projectile may behave as rigid or quasi-rigid (with mass loss due to abrasion), deformable and erosive. The projectile penetrates the concrete target either in a rigid or quasi-rigid mode when V0 is less than rigid body velocity (VR) or in an erosive mode when V0 higher than hydrodynamic velocity (VH) or in a deformable mode when VR ≤ V0 < VH. The rigid body velocity is determined to be the impact velocity at which dynamic strength of the penetrator times the cross-section area of the shank is equal to the current resultant target resistance force as the projectile nose shape changes from ogival to blunt; the hydrodynamic velocity is estimated to be the impact velocity at which a stable mushrooming head is formed on the basis of physical consideration. It transpires that the present model correlates well with available experimental data for concrete penetration.

On the penetration and perforation of concrete targets struck transversely by ogival-nosed projectiles - a numerical study

This paper carries out a numerical study on the penetration and perforation of (reinforced) concrete targets subjected to impact by ogival-nosed projectiles at normal incidence. A recently developed computational constitutive model for concrete subjected to dynamic loadings, which takes account of pressure dependency, strain hardening and softening, strain rate effects, Lode effect and failures in both high and low confining pressures, is employed in the numerical simulations. Parametric studies are performed numerically to examine the influences of impact velocity on the load-time histories in the case of semi-infinite concrete targets and the effects of impact velocity and concrete target thickness on the projectile residual velocities and the target cracking patterns in the case of finite reinforced concrete slabs. It transpires that the present model predictions are found to be in good agreement with experimental observations in terms of penetration depth, load-time history, residual velocity, impact cratering and scabbing size and pattern. It also transpires that the present model predicts better the sizes of both impact and scabbing craters than the modified K&C model and the modified HJC model even though these three models produce similar results for residual velocities.

Real-time numerical calculation for penetration depth of projectiles into concrete targets

ABSTRACTBased on the acceleration data measured by penetration experiments with ogive-nose projectiles into semi-infinite concrete targets, a fuzzy method which can calculate the real-time penetration depth was developed. In the proposed method, the whole process of penetration was divided into three stages according to the instantaneous velocity, and each stage was described by different models. By judging the calculation error, threshold velocities between stages were automatically determined. Meanwhile, the striking velocity of the penetration process was calculated using the acceleration in whole trajectory. The calculated values by model are in reasonably good agreement with the measured data from experiments.

The Prediction of the Depth of Long Rod Penetrating into Semi-Infinite Concrete Targets

Long rod has strong ability of penetrating into targets with high velocity because of the big ratio of L/D. In the process of the penetration, the resistance of target is so big that the deformation of the head of the projectile is severe. There are many factors influence the process, which make it difficult to get analytic solutions. In this paper, we propose a simplified calculation method which considering engineering strain of the head of projectile. And the rigid-plastic model was used to describe the constitutive model of projectiles. The relationship between the engineering strain of the mushroom area and velocity was analyzed, which is exponential. Then, combined with cavity expansion theory, the calculation results about the DOP are in good agreements with the experimental results. At last, there are numerical simulations about the relative experiments, and the results obtained from numerical simulations show the deformation of the projectile and the depth of the penetration, which are in good agreement with the theoretical calculation and experiments.

Response of steel-tube-confined concrete targets to projectile impact

Concrete is widely used in protective structures. Strength and toughness are two key factors for its anti-impact performance. Imposing constraint on concrete is an effective way to improve the anti-impact performance of concrete protective structures. In this paper, penetration tests of steel-tube-confined concrete (STCC) targets impacted by 12.7 mm armor piercing projectile (APP) at velocity around 820 m/s were conducted and different diameters and wall thicknesses of confining steel tube were considered. The typical damage modes of the tested STCC targets were obtained and influences of impact location, diameter and thickness of confining steel tube on the anti-penetration performance of STCC targets were also analyzed. The results show that the anti-penetration performance of STCC targets is obviously superior to that of semi-infinite concrete targets in restraint of the damage area and reduction of depth of penetration (DOP).

Dynamic spherical cavity expansion analysis of rate-dependent concrete material with scale effect

In this paper, dynamic spherical cavity expansion model is developed for rate-dependent concrete material described by modified Drucker-Prager Cap plasticity model incorporated with size effect. Penetration resistance components are computed accordingly with static resistance dependent on projectile diameter scale. Saturated region is introduced to investigate the response of concrete target under high impacting velocity. The validation of the proposed model is conducted by modelling a rigid projectile with full-scale and 1/10-scale diameter penetrating a semi-infinite concrete target. Depth of penetration numerically obtained is also compared with some widely recognized empirical penetration formulae, and better agreement is achieved by the proposed model for penetration tests with various striking velocities.

High Velocity Penetration of Concrete Targets with Eroding Long- Rod Projectiles; An Experiment and Analysis

This paper describes the design, analysis and experiments done to test eroding long-rod (9 ≤ L/d ≤ 11) penetration into semi-infinite concrete targets at high impact velocities (650 (m/s) &lt; v0 &lt; 1150 (m/s)). Furthermore, it studies the mechanical behavior of the projectile and semi-infinite concrete target at high velocity penetration. Test results showed similar qualities of eroding penetration in metal and concrete targets; therefore, it is possible to introduce models for studying eroding penetration in a semi-infinite concrete target using the basic equations used for evaluating penetration into metal targets. The experimental data on depths of penetration showed that the Forrestal model is inappropriate for studying eroding penetration in concrete targets; however these data are in good agreement with the results obtained from hydrodynamic theory. Therefore, it is recommended, that analytical study of eroding penetration in concrete targets takes account of necessary corrections relating to the special behavior of concrete when analytical models of penetration into metallic targets are used.