Ogive-nose Projectiles Research Articles

A Spherical Cavity Expansion Penetration Model for Concrete Based on Hoek–Brown Strength Criterion

Abstract A spherical cavity expansion model for concrete is first proposed by using an elastic-brittle-plastic material law with Hoek–Brown strength criterion. The constitutive model can capture the basic features of the mechanical response of concrete materials including the effects of strain-softening and pressure hardening (pressure-dependent shear strength) and all the parameters used in the model can be determined from material tests. The forcing function obtained from the spherical cavity expansion analysis is then employed to construct a penetration model for concrete targets struck by ogival-nosed projectiles. It transpires that the present model predictions are in good agreement with experimental observations in terms of penetration depth and ballistic limits/residual velocities in the case of perforation.

A Spherical Cavity Expansion Penetration Model for Concrete Based on Hoek–Brown Strength Criterion

Abstract A spherical cavity expansion model for concrete is first proposed by using an elastic-brittle-plastic material law with Hoek–Brown strength criterion. The constitutive model can capture the basic features of the mechanical response of concrete materials including the effects of strain-softening and pressure hardening (pressure-dependent shear strength) and all the parameters used in the model can be determined from material tests. The forcing function obtained from the spherical cavity expansion analysis is then employed to construct a penetration model for concrete targets struck by ogival-nosed projectiles. It transpires that the present model predictions are in good agreement with experimental observations in terms of penetration depth and ballistic limits/residual velocities in the case of perforation.

Mechanism of High-velocity Projectile Penetration into Concrete

Abstract The penetration depth of rigid projectiles is investigated using the modified spherical cavity expansion theory and the Holmquist–Johnson–Cook (HJC) model for the concrete targets, in which the model parameters used in the Mohr–Coulomb Tresca-limit yield criterion are obtained by the triaxial compression tests. By comparing the cavity expansion pressures of the concrete samples with two different types of aggregate, the influence of the aggregate hardness on the penetration processes is discussed. With the analysis of the tractions acted on the projectile nose, the influences of the projectile and target material properties as well as the projectile structure on the transition impact velocity are also discussed. By comparing the theoretical results with the experimental data, two penetration mechanisms are demonstrated for the ogive-nose projectile penetration into concrete with the striking velocities up to 2.0 km/s.

Mechanism of High-velocity Projectile Penetration into Concrete

Abstract The penetration depth of rigid projectiles is investigated using the modified spherical cavity expansion theory and the Holmquist–Johnson–Cook (HJC) model for the concrete targets, in which the model parameters used in the Mohr–Coulomb Tresca-limit yield criterion are obtained by the triaxial compression tests. By comparing the cavity expansion pressures of the concrete samples with two different types of aggregate, the influence of the aggregate hardness on the penetration processes is discussed. With the analysis of the tractions acted on the projectile nose, the influences of the projectile and target material properties as well as the projectile structure on the transition impact velocity are also discussed. By comparing the theoretical results with the experimental data, two penetration mechanisms are demonstrated for the ogive-nose projectile penetration into concrete with the striking velocities up to 2.0 km/s.

Mechanism of High-velocity Projectile Penetration into Concrete

Abstract The penetration depth of rigid projectiles is investigated using the modified spherical cavity expansion theory and the Holmquist–Johnson–Cook (HJC) model for the concrete targets, in which the model parameters used in the Mohr–Coulomb Tresca-limit yield criterion are obtained by the triaxial compression tests. By comparing the cavity expansion pressures of the concrete samples with two different types of aggregate, the influence of the aggregate hardness on the penetration processes is discussed. With the analysis of the tractions acted on the projectile nose, the influences of the projectile and target material properties as well as the projectile structure on the transition impact velocity are also discussed. By comparing the theoretical results with the experimental data, two penetration mechanisms are demonstrated for the ogive-nose projectile penetration into concrete with the striking velocities up to 2.0 km/s.

Penetration and Perforation of Thick Targets of Open-Cell and Closed-Cell Aluminum Foams by Ogival-Nosed Projectiles

Penetration and Perforation of Thick Targets of Open-Cell and Closed-Cell Aluminum Foams by Ogival-Nosed Projectiles

High Velocity Impact Behaviour of Hybrid-Fiber Engineered Cementitious Composite Panels

High-velocity impact behaviour of hybrid-fibre engineered cementitious composite (ECC) panels subjected to an impact from a hardened steel, ogive-nosed projectile at velocities between 300-700 m/s is investigated and reported in this paper. The new ECC mix contains a proportion of 0.75% volume high-modulus steel fibres and 1.25% volume low modulus polyvinyl-alcohol (PVA) fibres. The mix is designed to achieve a desired balance between the strain hardening behaviour and impact resistance of material required for impact and blast resistant structures. The new hybrid-fibre ECC demonstrates its excellent capability for impact resistance and strong potential as a protective material with reduced impact damage and distributed micro cracking.

Projectile Nose Mass Abrasion of High-Speed Penetration into Concrete

Based on the dynamic spherical cavity expansion theory of concrete and the analysis of experimental data, a mass abrasion model of projectile considering the hardness of aggregates, the relative strength of target and projectile, and the initial impact velocity is constructed in this paper. Furthermore, the effect of mass abrasion on the penetration depth of projectile and the influence of hardness of aggregates and strength of projectile on penetration depth and mass loss are also analyzed. The results show that, for the ogive-nose projectile with the CRH of 3 and aspect ratio of 7 penetrating the concrete of 35 MPa, the “rigid-body penetration” model is available when the initial impact velocity is lower than 800 m/s. However, when the initial impact velocity is higher than 800 m/s, the “deforming/eroding body penetration” model should be adopted. Through theoretical analysis and numerical calculation, the results indicate that the initial impact velocity is the most important factor of mass abrasion. The hardness of aggregates and the strength of projectile are also significant factors. But relatively speaking, the sensitivity of strength of projectile to mass abrasion is higher, which indicates that the effect of projectile material on mass abrasion is more dramatic than the hardness of aggregates.

Effect of target span and configuration on the ballistic limit

Three-dimensional numerical simulations were carried out with ABAQUS/Explicit finite element code to study the influence of target span and configuration on its ballistic limit. 1 mm thick 1100-H12 aluminum targets of varying span diameter and configuration were impacted by blunt and ogive nosed projectiles of 19 mm diameter and 52.5 g mass. The effect of target span was studied by varying the span diameter of 1 mm thick monolithic target as 50 mm, 100 mm, 204 mm, 255 mm and 500 mm. The effect of configuration was studied by taking the monolithic, double layered in-contact and double layered spaced targets of 1 mm equivalent thickness and 255 mm span diameter. The spacing between the layers was varied as 2 mm, 5 mm, 10 mm, 20 mm and 30 mm. In each case the target was impacted normally by blunt and ogive nosed projectile to obtain the ballistic limit. The highest ballistic limit was observed for monolithic target followed by layered in-contact and spaced targets respectively. The variation of spacing between the layers did not have significant influence on the ballistic limit in the case of ogive projectile but some effect was seen in the case of blunt projectile. The ballistic limit was found to increase with increase in target span diameter for both the projectiles and it was found to be higher for blunt nosed projectile as compared to that of ogive nosed projectile for all the spans considered excepting in the case of 50 mm span for which it was higher for ogive nosed projectile.

A spherical cavity expansion model for penetration of ogival-nosed projectiles into concrete targets with shear-dilatancy

A dynamic spherical cavity-expansion penetration model is suggested herein to predict the penetration and perforation of concrete targets struck normally by ogivalnosed projectiles. Shear dilatancy as well as compressibility of the material in comminuted region are considered in the paper by introducing a dilatant-kinematic relation. A procedure is first presented to compute the radial stress at the cavity surface and then a numerical method is used to calculate the results of penetration and perforation with friction being taken into account. The influences of various target parameters such as shear strength, bulk modulus, density, Poisson’s ratio and tensile strength on the depth of penetration are delineated. It is shown that the model predictions are in good agreement with available experimental data. It is also shown that the shear strength plays a dominant role in the target resistance to penetration.

Evaluation of the Impact Formulae for Rigid Projectile Striking on Concrete Target

Based on the large amounts of field impact tests with different projectile nosed shapes, the abilities of the existing classical empirical and semi-empirical impact formulae in predicting the local damage of normal and high strength concrete targets (NSCT & HSCT) under the strike of rigid projectile were evaluated. It finds that, firstly, for the penetration depth, the Forrestal and Chen & Li semi-empirical formulae, BRL and Whiffen empirical formulae are advised for the NSCT under the impact of ogive nosed projectile; and Chen & Li semi-empirical formula and ACE empirical formulae are advised for the NSCT under the impact of special nosed projectile; the dimensionless penetration depth of NSCT increases linearly with the non-dimensional impact factor. Secondly, for the penetration depth, Chen & Li semi-empirical formula is advised for the HSCT under the mid-to-high speed impact, and the existing formulae are not applicable while the speed of the projectile was relatively low. Thirdly, for the perforation mode of the target, the BRL and Chang empirical formulae are advised for the NSCT, and the Chen semi-empirical formula, ACE and BRL empirical formulae are advised for the HSCT.

Computer-Aided Design of Protective Structures: Numerical Simulations and Experimental Validation

This paper aims through several numerical studies to highlight some effects of layering plates in ballistic protection. The possible increase in perforation resistance by varying the material properties of the plates, the individual plate thickness (the total plate thickness is constant) and the stacking of individual plates in a double-layered target when struck by blunt and ogival nose projectiles has been investigated. This was done by conducting non-linear finite element simulations of the perforation process using an experimentally validated numerical model and an explicit finite element code. These studies are difficult to carry out experimentally due to the many materials and thicknesses involved and computer-aided design is thus an attractive approach. The numerical design indicates that it is possible to considerably increase the overall ballistic protection level by using double-layered plates and a proper design. Some of the most promising designs were then selected for experimental validation. The experimental tests gave completely opposite results than the computer-aided design, and the reasons for this will be discussed in some detail.

A semianalytical and numerical study of penetration and perforation of an ogive-nose projectile into concrete targets under normal impact

In this article, a semianalytical model is proposed to predict the penetration depth of an ogive-nose projectile into a concrete target. In addition, the theory of shear plugging is used to calculate the residual velocity of the projectile following complete perforation of the target. In this analysis, which is based on the Forrestal model, conservation of energy was employed to determine the axial forces on the projectile and target during both the penetration and perforation stages and the governing equations were derived in each case. The tests were then simulated numerically with the finite element code LS-DYNA and good agreement was obtained with both experimental data and the predictions of the analytical model.

Tensile Strength versus Toughness of Cement-Based Materials against High-Velocity Projectile Impact

This paper presents a laboratory experimental study on the effect of tensile strength and toughness on the resistance of cement-based materials to high-velocity projectile impact. Three types of cement-based materials with similar compressive strength but different tensile strengths and toughnesses were examined in terms of the penetration depth, crater diameter, and crack propagation in specimens subjected to impact of ogive-nosed projectile with a diameter of 13.35 mm and a mass of 19 grams traveling at velocities of about 650 m/s. The materials evaluated include: (i) a plain high-strength concrete (HSC) with low tensile strength and toughness, (ii) a fiber-reinforced concrete (FRHSC) with high toughness but similar flexural tensile strength as the HSC, and (iii) a polymer cement composite (PCC) with high flexural tensile strength but low toughness. The PCC was developed from a combination of inorganic cements with water-soluble polymers, and it had a 28-day flexural tensile strength of 25 MPa. Results suggest that the toughness was a more important parameter that contributes to the impact resistance of the cement-based materials. Increasing the tensile strength alone, however, did not seem to contribute to the impact resistance of the cement-based materials.

Theoretical Approach in Predicting Perforation of Aluminum Alloy Foam Target against Different Ogive-Nosed Projectile

This paper presents a theoretical approach for investigating the perforation of aluminum alloy foam target against rigid ogive-nosed projectile. The target is composited by two different density single-layer aluminum alloy foam boards. The dynamic cavity expansion theory is applied to formulate analytical model. The perforating process can be divided into 8 stages. The effects of shank diameter, shank length and caliber-radius-head (CRH) on perforating resistance force and kinetic energy variation are analyzed. The results demonstrate that velocity limit increases significantly with the raising of shank diameter in the case of fixed mass and CRH has no significant influence on residual velocity and velocity limit. And the residual velocity can be predicted by the known striking velocity and velocity limit.

A Numerical Method for Penetration into Concrete Target Using SPH-Lagrange Coupling Method

This paper demonstrates the application of both numerical simulation and empirical equation in predicting the penetration of a concrete target by an ogive-nosed projectile. The results from the experiment performed by Gran and Frew are used as a benchmark for comparison. In the numerical simulations a 3.0-caliber radius-head steel ogival-nose projectile with a mass of 47 kg is fired against cylindrical concrete target with a striking velocity of 315 m/s. In the simulation the smooth particles hydrodynamics SPH-Lagrange coupling method is applied to predict the maximum depth of penetration. For calculation of DoP and response of projectile the SPH-Lagrange method can give satisfactory results.

Triaxial Acceleration Measurement for Oblique Penetration Into Concrete Target

To obtain accurate data of the motion parameters of a rigid projectile during the oblique penetration event, a triaxial acceleration measurement device (TAMD) was developed, and a method for the calibration of a high-g accelerometer was presented by using a Hopkinson bar and a grating laser Doppler interferometer. The buffer structure was designed, and the cushioning capacity of it was studied to improve the survivability of the multichannel data recorder. A set of penetration experiments with concrete targets that had average compressive strengths of 35 and 45 MPa was conducted to characterize the response of monolithic concrete targets to projectile impact. The 96-mm-diameter 630-mm-long ogive-nose projectiles were machined from 35CrMnSiA steel and designed to contain a TAMD in the tail of the cavity. The projectiles were launched by a 100-mm-diameter smooth-bore powder gun to striking velocities between 300 and 600 m/s, and impacted the concrete target at an oblique angle of 0°-30°. The acceleration during the launch and the triaxial deceleration during the penetration were successfully recorded by the TAMD. The measured penetration data and deceleration-time data were analyzed.

Estimation of Deep Penetration Resistance with Spherical Specific Cavitation Energy

A simple model is suggested for deep penetration resistance of rigid, axially-symmetric, nose-pointed projectiles penetrating ductile metal targets. Model is based on power balance between the power supplied by the projectile during steady-state penetration and elastoplastic power needed for expanding penetration hole. The latter is approximated with the aid of the spherical specific cavitation energy (spherical cavitation pressure). Frictionless model includes an empirical parameter which is found to be practically independent of target material characteristics but reflects the shape of head profile. For ogival nose projectiles (with the spherical nose as a special case) the empirical parameter values are limited to a narrow range, slightly lower than one. Friction resistance is included by the Prandtl friction model leading to a general expression for the deep penetration hardness. Experimental data of spherical and ogival nose projectiles penetrating aluminium targets is compared with analytical predictions for penetration depth and an optimal ogival nose projectile is discussed.

Ballistic Limit Predictions with Quasi-Static Cavitation Fields

Recent work on ductile hole enlargement under plane-stress conditions has revealed that while the internal pressure does not reach a saturation level, the energy increment required to create a nominal hole volume increment admits a finite asymptotic value. This specific cavitation energy, which is identified with the cavitation pressure required for plane-strain and spherical cavitation patterns, suggests a possible new view of cavitation states in energetic terms. Based on the specific cavitation energy the ballistic limits of monolithic targets are estimated from a simple energy balance and residual velocities are found from the Recht-Ipson formula. This plate perforation model is independent of projectile head profile and neglects friction. Albeit the simplicity, comparison with experimental and numerical data from various sources, for conical and ogival-nose projectiles, shows good agreement. In fact, over a practical range of h/ D ratio, residual velocities are bounded between plane-stress and plane-strain predictions, gradually shifting from plane-stress limit to plane-strain bound as h/ D increases. Spherical cavitation fields are also discussed in conjunction with limits of validity of cavity expansion models and connection between plane-stress cavitation and the ultimate tensile stress is demonstrated.

Development of functionally-graded cementitious panel against high-velocity small projectile impact

A functionally-graded (FG)-cementitious panel consisting of PE-fibrous ferrocement, calcined bauxite aggregates and conventional mortar was developed to resist high-velocity small projectile penetration. A total of 72 specimens measuring 200 mm by 200 mm by 100 mm were fabricated and subjected to ogive-nosed (Caliber Radius Head, CRH = 2.5) projectile impacts at velocities ranging from 300 m/s to 600 m/s. The results indicated that FG-panels have superior impact resistance compared to plain mortar targets in which all FG-panels remained intact, whereas the latter disintegrated into several pieces when the projectile velocity exceeded 300 m/s. The FG-panels also suffered minor front face damages with much smaller average crater diameters (<48 mm) compared to plain mortar targets (>100 mm). However, penetration depths in the FG-panels were slightly larger at impact velocity less than 400 m/s compared to the mortar panels due to the lower compressive strength of PE-fibrous ferrocement. At higher impact velocity, all penetration depths in FG-panels were smaller than those in plain mortar targets. The effects of thickness variation of each functional layer were also investigated and results showed that thickening the calcined bauxite aggregate layer was most effective in reducing the penetration depth for all impact velocities, but the average inner and outer crater diameters were slightly increased.