Rigid Projectile Research Articles

A fractal comminution approach for scaling issues of penetration failure of concrete target

This paper presents a comprehensive analysis of the scaling issue for the penetration problem of concrete target impacted by a rigid projectile. The mechanisms of failure and comminution are proposed for the analysis of resistant stress of the concrete target. By introducing the fractal theory for the comminution, the formula of quasi-static resistant stress is derived. The fracture energy and the scaling term are well included in the derived formula without further empirical assumptions. The experiments of 7 projectiles and concrete targets of 2 strength grades were performed. The proposed formula is validated by our experimental data and the classic empirical models.

An approximate contact pressure for normal penetration of rigid ogive projectiles into metal targets

An approximate analytical expression for the contact pressure applied by a metal target to a rigid ogive projectile is determined by generalizing the analytical expressions developed previously for penetration of a rigid ovoid of Rankine into an incompressible elastic-perfectly-plastic target. Two empirical shape factors are introduced and determined which model the geometric dependences of the terms in the contact pressure due to the target’s yield strength and inertia. Analytical expressions are determined for the resistance to penetration which depend on the ogive’s shape and which determine the critical penetration velocity for the onset of separation of the target material from the projectile’s nose. Also, a procedure for determining the effective yield strength of a general target material is presented. Results of numerical simulations for different ogives and different target materials are used to validate the proposed analytical equations. Some results are compared with experimental data.

A Numerical Study on the Oblique Penetration of Spherical-Nosed Rigid Projectiles into Semi-Infinite Metallic Targets

A Numerical Study on the Oblique Penetration of Spherical-Nosed Rigid Projectiles into Semi-Infinite Metallic Targets

Experimental Study on Local Damage to Reinforced Concrete Panels Subjected to Oblique Impact by Projectiles

Abstract Most empirical formulas used to evaluate local damage to reinforced concrete (RC) structures have been based on impact tests conducted with a rigid projectile at an impact angle normal to the target structure. Only a few impact tests have been performed involving a soft projectile. Therefore, in this study, we conducted a series of impact tests to evaluate the local damage to RC panels subjected to normal and oblique impacts by rigid and soft projectiles. This paper presents the test conditions, test equipment, test results, and obtained knowledge on local damage to RC panels subjected to normal and oblique impacts.

Effect of combined gradation in cross-sectional area and density on the dynamic compressive behavior of foams for moderate impact velocities

The effect of combined gradation in area and density on the dynamic response of foams is studied in this work. The cross-sectional area and density are graded such that the product of these quantities results in a tri-linear variation along the foam’s length, and hence, the foam type is designated as Type-TL. A theoretical model based on the R-PP-L idealization is developed to study the response of the Type-TL foam struck by a rigid projectile. The Type-TL foam offers force distribution over a considerably larger area than a homogeneous foam, which may benefit structural protection.

More on the penetration of spherical-nosed rigid projectiles into metallic targets

This work deals with several issues related to the deep penetration of spherically nosed rigid projectiles impacting metallic targets at normal incidence. The most important issues in these processes are the constant resisting stress acting on the projectile beyond the initial entrance phase, the extent of the entrance phase, and the onset of cavitation at impact velocities higher than a certain threshold velocity. In this work, we derive a new relation for the target’s resisting stress in terms of its bulk and shear moduli and we also use a simplified analysis to account for the effect of the entrance phase on the depth of penetration for spherically nosed rigid projectiles. In addition, we highlight the role of cavitation in this process through numerical simulations for targets having very different densities.

Penetration trajectory of rigid projectile in the heterogeneous meso-scale concrete target

For the normal penetration of a symmetrical rigid projectile into a concrete target with coarse aggregates, the lateral deflection may occur under certain conditions depending on geometrical parameters of the projectile, impact velocity and coarse aggregate distribution. In this work, four dimensionless numbers of projectile, that is, impact factor [Formula: see text], length-to-diameter ratio [Formula: see text], nose factor [Formula: see text] and the relative location of mass center [Formula: see text], are employed to study the effects of projectile parameters on the deflection of penetration trajectory. Numerical studies based on three-dimensional (3D) meso-scale concrete model are conducted and the projectile trajectories are obtained under different dimensionless numbers. According to the development of the deflection angle during the rigid projectile penetration into meso-scale concrete, the motion of the projectile can be divided into four stages, that is, initial deflection, rapid change, deflection rebound and final stage. The numerical results show that, for the same meso-scale concrete target, the deflection of the projectile trajectory becomes larger with the increases of [Formula: see text], [Formula: see text] and [Formula: see text], while the deflection angle of projectile decreases with the increase of [Formula: see text].

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.

Numerical Simulation Study on Relationship between the Fracture Mechanisms and Residual Membrane Stresses of Metallic Material.

The distribution and dissipation energies in fracture mechanisms were a critical challenge to derive, especially for this ultra-thin sample. The membrane failure, which is the end of the fracture mechanisms, is a result of the cone wave reflections from the backend membrane boundaries. These reflections delay the failure processes due to the shock impacts. To compare these results with the experimental work, a numerical simulation was conducted for these processes. The cylinder-shaped rigid projectile was impacted using a frictionless Lagrange solver. The target was a cartridge brass circle plate clamped at its perimeter, and its zone was refined to a ten-times higher meshing density for better analysis. The erosion and cut-off controls involved a zero-gap interaction condition and an instantaneous geometric erosion strain of 200%. Due to the maximum projectile velocity of 382 m/s having the slowest perforation, the target thickness was found to be 5.5 mm. The fracture mechanism phenomena, such as tensile, compressive, through-thickness, and growth in-plane delamination, propagating delamination, and local punch shear waves were observed. After deducting tensile and flexural strengths from the last experiment, a total residual membrane stress of 650 MPa was found. This result indicated a relationship between the fracture mechanisms and residual membrane stresses of metallic material.

A Machine Learning Model for the Prediction of Concrete Penetration by the Ogive Nose Rigid Projectile

In recent years, research interest has been revolutionized to predict the rigid projectile penetration depth in concrete. The concrete penetration predictions persist, unsettled, due to the complexity of phenomena and the continuous development of revolutionized statistical techniques, such as machine learning, neural networks, and deep learning. This research aims to develop a new model to predict the penetration depth of the ogive nose rigid projectile into concrete blocks using machine learning. Genetic coding is used in Python programming to discover the underlying mathematical relationship from the experimental data in its non-dimensional form. A populace of erratic formulations signifies the rapport amid dependent parameters, such as the impact factor (I), the geometry function of the projectile (N), the empirical constant for concrete strength (S), the slenderness of the projectile (λ), and their independent objective variable, X/d, where X is the penetration depth of the projectile and d is the diameter of the projectile. Four genetic operations were used, including the crossover, sub-tree transfiguration, hoist transfiguration, and point transfiguration operations on supervised test datasets, which were divided into three categories, namely, narrow penetration (X/d < 0.5), intermediate penetration (0.5 ≤ X/d < 5.0), and deep penetration (X/d ≥ 5.0). The proposed model shows a significant relationship with all data in the category for medium penetration, where R2 = 0.88, and R2 = 0.96 for deep penetration. Furthermore, the proposed model predictions are also compared with the most commonly used NDRC and Li and Chen models. The outcome of this research shows that the proposed model predicts the penetration depth precisely, compared to the NDRC and Li and Chen models.

Experimental and Analytical Study on the Penetration Depth of Mortar Targets Subjected to Projectile Impact in the Hypervelocity Regime

A projectile may be deformed and eroded due to the high pressure generated by hypervelocity penetration, which makes it difficult to describe the penetration mechanism for protection engineering by existing theories at such high velocities. To analyze the penetration depth of concrete-like targets subjected to hypervelocity impact by kinetic energy weapons, experiments with ogive-nosed steel projectiles penetrating mortar targets are conducted, where the average uniaxial compressive strength of the mortar targets is 41.8[Formula: see text]MPa and the impact velocities range from 1[Formula: see text]225[Formula: see text]m/s to 2[Formula: see text]392[Formula: see text]m/s. The experimental results show that the crater diameter and crater depth have a linear relationship with the striking velocity. The depth of penetration (DOP) increases linearly first and then decreases sharply and increases slowly again. Three penetration regimes are observed in turn with increasing velocity, i.e. rigid projectile penetration, abrasive projectile penetration and semifluid projectile penetration. Furthermore, based on a study of the dynamic compression behavior and penetration resistance function of concrete, a hydroelastoplastic-frictional penetration model is established. The velocity range is divided into solid penetration, semifluid penetration and fluid penetration, which correspond to [Formula: see text], [Formula: see text] and [Formula: see text], respectively. Then, the rigid and abrasive projectile penetration models, which consider the projectile mass loss, are verified by the present test data. Finally, the semifluid projectile penetration model is evaluated with the existing test data. These results can provide support for research on the damage effect of hypervelocity kinetic energy weapons and the design of underground strategic protection engineering.

Use of compliant actuators for throwing rigid projectiles.

Muscles and tendons, actuators in robotics, and various sports implements are examples that exploit elasticity to accelerate objects. Tuning the mechanical properties of elastic elements connecting objects can greatly enhance the transfer of mechanical energy between the objects. Here, we study experimentally the throw of rigid projectiles by an actuator, which has a soft elastic element added to the distal end. We vary the thickness of the elastic layer and suggest a simple mass-spring chain model to find the properties of the elastic layer, which will maximize the energy transfer from the actuator to the projectile. The insertion of a soft layer, impedance matched to the ejection frequency of the projectile mass, can increase the throwing efficiency by over 400%. Finally, we identify that very thick and very soft compliant layers could potentially lead to high efficiency and flexibility simultaneously.

The optimal nose shape of a rigid projectile deeply penetrating into a solid target considering friction

The paper deals with the optimal nose shape of a perfectly rigid axi-symmetric projectile which deeply penetrates into a semi-infinite target accounting for the dry friction between the nose surface and the target. Analytical expressions of the contact stresses at the “projectile-target” interface and of the total resistance force as well as of the final penetration depth are developed for targets described by a locked hydrostat and a linear shear failure-pressure relationship. These analytical expressions are developed using the cylindrical cavity expansion (CCE) and the spherical cavity expansion (SCE) approaches. A comparison of these approaches on the optimization problem solution is performed. The effect of dry friction on the optimal shape of the projectile nose is investigated and two main approaches to solving the problem of shape optimization are studied. Two optimization approaches are compared: the first optimization approach is based on minimizing the resistive force (MRF) acting on the projectile, and the second approach is based on maximizing the penetration depth (MPD). The optimal shapes are compared for a fixed shank radius and evaluations are carried out for different nose lengths and different values of the coefficient of friction. It is shown that friction may have a visible effect on the final penetration depth, although in all cases, the friction effect on the optimal shape of the projectile nose is negligible. The obtained optimal nose shapes are implemented in computational analysis in an own developed code that had been verified with numerous test data to examine whether these shapes actually lead to a minimum resistive force and to a maximal penetration depth. Significant effectiveness of the optimal shape performance is shown for larger radius projectiles having a defined nose length.

Numerical analysis of ballistic impact through FE and SPH methods

In the defense and aerospace industries, structures are designed to resist ballistic impact loads. Experimental analysis of ballistic impact has been conducted successfully for many years, and alternatively, numerical techniques have been employed to reduce the experimental cost. In this study, the ballistic impact of metallic materials is addressed with both finite element (FE) and smoothed particle hydrodynamics (SPH) methods. A single-shot ballistic impact model consisting of a deformable plate and a rigid projectile is developed. These two methods are compared using Johnson-Cook (JC) and Modified Mohr-Coulomb (MMC) damage models. Lode parameter dependent MMC damage criterion is implemented in the user-defined field (VUSDFLD) for damage analysis. Various numerical setups with varying target thickness, impact velocity, projectile nose shape and impact angle of the projectile, are generated. The damage response of the plate target according to the impact angle and the nose shape and the effect of ballistic impact parameters on the residual velocity is discussed in detail. The results are compared with the experimental results from the literature. FE method is found to be more consistent than SPH method in the prediction residual velocity. MMC damage model is better in agreement with experimental data than JC damage model. A linear decrease in residual velocity is observed with increasing thickness of target except the JC model used with FE method. Moreover, blunt projectiles are more sensitive to change in the impact angle than hemispherical and ogival projectiles. Increase in impact angle cause a reduction in residual velocity for all three projectile.

A model for rigid asymmetric ellipsoidal projectiles penetrating into metal plates

A theoretical model is presented for penetration of asymmetric ellipsoidal projectiles which are proposed to fit the lift-generating outline of hypersonic vehicles. The projectile is composed of two triaxial quarter ellipsoids with one different semiaxis, and four geometric parameters are required to decide the shape. The model is based on two-term drag equation and a stress distribution relation of elliptical boundary with hole enlargement mechanism. Verification of the model is completed by simulation cases of six different projectiles with initial velocity between 600 m/s to 1000 m/s. Ballistic characteristics of asymmetric ellipsoidal projectiles including acceleration and residual velocity are derived from the model and analyzed to acquire the effects of geometric parameters on penetration results. Two decisive factors of cross section shapes, asymmetry and flatness, are specially discussed in contributions to residual velocity. Comparations with traditional circular cross-sectional cases are also presented, which indicates that same penetration capacity could be retained in the asymmetric ellipsoidal projectiles as in the circular cross-sectional one by selecting the shape controlling factors.

Dynamic response of density-graded foam subjected to soft impact

The density-graded foam materials are gaining traction due to their enhanced impact and blast resistance capacities. However, current knowledge in the impact response of density-graded foam is limited to rigid impact, which narrows the design space of target materials. In particular, three main issues remain unclear, i.e., (1) how to quantify soft impact response, (2) what is the reduction of deformation and transferred stress from soft impact as compared to rigid impact, (3) whether density-graded foam can reduce the transferred stress from soft impact. To address these knowledge gaps, an analytical model based on the double shock wave theory is established by using a deformable projectile impinging onto a density-graded foam target. The dynamic stress at the supported end is analyzed for uniform, positive, and negative density gradients. The results indicate that the deformation process due to impact from deformable projectile is vastly different from that of traditional rigid projectile, with the former causing 27.42% smaller deformation and 9.87% stress reduction of the graded foam target, and three separate velocities can be observed throughout the soft impact process. The findings indicate lower mechanical requirements of target materials for soft projectile impact protections, potentially leading to weight and cost savings.

More on the perforation of concrete slabs by rigid projectiles

We demonstrate the validity and usefulness of our recently-published model for the perforation of concrete slabs by rigid projectiles. The model also accounts for the scaling issue in concrete penetration/perforation, which presented a longstanding obstacle in modeling the concrete's response to projectile impact. Comparing predictions of the model with several sets of data on concrete slab perforation, show very good agreement as far as ballistic limits and residual velocities are concerned.

Modelling the penetration of subsonic rigid projectile probes into granular materials using the cavity expansion theory

Typical subsurface investigation tools used on Earth are not applicable for subsurface exploration of the Moon and other extraterrestrial bodies due to payload limitations in space missions. Instead, light and compact subsonic projectile probes can be considered as an alternative subsurface investigation tool in such exploratory missions to overcome a host of challenges. Such probes can be launched from a lunar orbiter or lander to the surface of the Moon to provide the initial effective penetration from the impact. Here, we develop a model based on the spherical cavity expansion theory to predict the deceleration rate and final penetration depth of a rigid projectile probe into geological targets under the perpendicular subsonic impact. Two stress fields are assumed to propagate in the medium, plastic (near field) and elastic (far field), upon the impact. The stresses at the cavity wall are obtained by combining the Mohr–Coulomb failure criterion for the target failure (plastic region) considering two different assumptions for plastic wave propagation. Two field experiments are used to compare and assess the robustness of the proposed solutions in the subsonic range. Base on the simulation results and the experiments, it is concluded that the cavity expansion model considering the locked hydrostat assumption, with the modification here introduced for the volumetric strain, can provide us with a reasonable prediction of the projectile penetration, final penetration depth and the stresses on the probe. Thus, our proposed solution can be used as a benchmark for sophisticated and computationally-expensive numerical calculations.

Experimental study of the resistance of RC walls with different transverse reinforcements subjected to large-scale rigid projectile impacts

After the 9/11 terrorist attacks, the nuclear power plants (NPPs) containment resisted a commercial aircraft or wind-borne missile impact has become one of the focus issues in the nuclear security field. Transverse reinforcement is typically used in reinforced concrete (RC) walls for nuclear engineering. However, there is little research related to the damage characteristics of RC walls with transverse reinforcement under the impact of a large-scale rigid projectile, and the effect of transverse reinforcement on penetration or perforation under projectile impact is still unclear. In this paper, according to different forms of transverse reinforcement, three types of RC walls were designed, and a total of eight large-scale rigid projectile impact tests for RC walls were performed. The failure mode of the walls, the concrete scabbed area, the penetration depth and the total failure number of longitudinal reinforcement were measured for comparison. The conclusion is that the form of transverse reinforcement influences the failure mode of an RC wall subjected to a rigid projectile impact. Transverse reinforcement plays a significant role in reducing the rear scabbing of the concrete. The tested walls with U-shaped transverse reinforcement show better performance than the walls in the form of classic stirrups with hooks with regard to perforation capacity under rigid projectile impact. In addition, the dynamic response characteristics of RC walls subjected to large-scale rigid projectile impacts are analyzed preliminarily, and the impact test results are consistent with the predictions of the Chang’s empirical formula on damage modes. The related works and conclusions can provide a basis for NPP structural optimization and the safety assessment of large commercial aircraft collision problems and can also provide experimental data to verify finite element methodology.

Behavior of High-Strength and Ultrahigh-Performance Concrete Targets Subjected to Relatively Rigid Projectile Impact

AbstractThis experimental study was conducted to evaluate the impact behavior of relatively rigid projectiles with conical and hemispherical nose shapes on normal to high-strength and ultrahigh per...