On hypervelocity penetration of the mesh-bumper strings into a projectile

An elastic–plastic model describing hypervelocity penetration of a mesh-bumper string by an arriving projectile is presented. An analytical solution for the case of rigid penetration is derived whereby the dependence between penetration depth and impact velocity is established. A comparative analysis between rigid penetration and penetration with a spreading string is performed. The mesh strings interact between each other with the aid of flow arising during penetration. The model which is developed allows us to estimate destruction depth of the projectile during its interaction with the mesh strings.     

High-speed penetration of a projectile into aluminum alloys at low temperatures

In order to elucidate the impact-induced fractures of materials used in outer space and manufacturing plants in low-temperature environments, the penetration and perforation of three kinds of aluminum alloys, A2017, A7075, and A5056 at room temperatures and low temperatures in the velocity range from about 500 m/s to 1.8 km/s were investigated experimentally. Main interests were focused on the depth and diameter of craters and experimental equations for the relationship between them and impact velocity were proposed. Also, microscopic observation of the recovered specimens and some numerical simulations of the penetration process were made. As a result, very distinctive features of the temperature effect on the high-speed fractures were found.     

Numerical simulations of oblique-angle penetration by deformable projectiles into concrete targets

Numerical simulations of oblique-angle penetration by deformable projectiles into concrete targets are performed in this paper by using the three-dimensional finite element code LS-DYNA, into which a combined dynamic constitutive model which can simultaneously describe both the compressive and tensile damage of concrete is implemented. As a consequence, the ballistic trajectories and the depths of penetration under different oblique angles (from 10° to the ricochet angle) are obtained. Moreover, the damage distribution of concrete after oblique penetration is procured, which can really reflect the tensile and compressive damage of concrete. The numerical results for the depths of penetration are compared with experimental data obtained by previous authors and show good agreement.     

Hypervelocity penetration of concrete

Experiments have been conducted with 6.25 mm diameter tungsten rods striking concrete at 2.2 km/s. Three concretes were used—one was 2.35 g/cm³ and the other two were 2.27 g/cm³. The erosion rates were measured to be T/ΔL = 2.4–3.1 depending on the density of the concrete. This is greater than the hydrodynamic value, which shows that the strength of the penetrator is affecting the penetration. The cratering efficiency was computed (which included surface spall) and was found to be commensurate with the strength of the concrete, 28–34 MPa. CTH calculations were conducted using the brittle fracture kinetics (BFK) and Holmquist–Johnson–Cook (HJC) material models for concrete. Density in the calculations was 2.25 g/cm³. It was not possible to match erosion rates at 2.2 km/s, which were too high in the calculations. Also, computed crater volumes were much too small, mainly due to spall in the experiments that was not shown in the computations. Another significant inaccuracy of the calculations was the damage extent, which became unrealistically widespread as time increased in the BFK model.     

Investigation on the response of segmented concrete targets to projectile impacts

The study of penetrator performance without free-surface effects can require prohibitively large monolithic targets. One alternative to monolithic targets is to use segmented targets made by stacking multiple concrete slabs in series. This paper presents an experimental investigation on the performance of segmented concrete targets. Six experiments were carried out on available small scale segmented and monolithic targets using instrumented projectiles. In all but one experiment using stacked slabs, the gap between slabs remained open. In the final experiment design, grout was inserted between the slabs, and this modification produced a target response that more closely represents that of the monolithic target.     

High velocity penetration of homogeneous, segmented and telescopic projectiles into alumina targets

Segmented and telescopic projectiles are designed to make efficient use of the higher impact velocities achievable with new acceleration techniques. This concept has been found to work against steel armour. In this study, we compare the penetration capability into an alumina target for these unconventional projectiles with that of a homogeneous projectile. The influence of segment separation distance and core-to-tube diameter ratio were simulated for the impact velocities 2.5, 3.0 and 3.5 km/s. The simulated final penetrations are compared to test results for one type of each of the homogeneous, segmented and telescopic projectiles at 2.5 and 3.0 km/s. Both simulations and tests show that the unconventional projectiles have better penetration capability than a homogeneous projectile with the same initial geometry.     

A fuzzy model of the penetration resistance of concrete targets

The penetration resistance of a concrete target varies greatly with the strike velocity of the projectile from low and intermediate impact velocities to high impact velocities. A fuzzy model of the penetration resistance of a concrete target is proposed to describe this characteristic. A complete analysis is conducted of the penetration process during which a rigid projectile penetrates a semi-infinite concrete target based on the proposed fuzzy model. Good agreement is observed between the experimental and predicted results based on the proposed fuzzy model.     

Multiple impact penetration of semi-infinite concrete

An experimental study was performed to gather multiple impact, projectile penetration data into concrete. A vertical firing range was developed that consisted of a 30-06 rifle barrel mounted vertically above a steel containment chamber. 0.41 m cubes of an Air Force G mix concrete were suspended in wet sand and positioned in the steel chamber. The concrete targets were subjected to repeated constant velocity impacts from 6.4 mm diameter steel projectiles with an ogive nose shape and a length to diameter ratio of 10. A laser sight was adapted to the rifle to ensure alignment, and a break screen system measured the projectile velocity. After each impact, the projectile penetration and crater formation parameters were recorded. The penetration and crater formation data were consistent with single impact penetration data from previous studies conducted at Sandia National Laboratories. In addition, an analytic/empirical study was conducted to develop a model that predicted the penetration depth of multiple impacts into concrete targets. Using the multiple impact penetration and crater formation data, a single impact penetration model, developed by Forrestal at Sandia National Laboratories, was extended to account for the degradation of the target strength with each subsequent impact. The degradation of the target was determined empirically and included in the model as a strength-modifying factor. The model requires geometry parameters of the ogive nose projectile, projectile velocity, the number of impacts, and target compressive strength to calculate the overall penetration depth of the projectile.     

Numerical modeling of projectile penetration into compressible rigid viscoplastic media

We develop computational methods for modeling penetration of a rigid projectile into porous media. Compressible rigid viscoplastic models are used to capture the solid–fluid transition in behavior at high strain rates and account for damage/plasticity couplings and viscous effects that are observed in geological and cementitious materials. A hybrid time discretization is used to model the non‐stationary flow of the target material and the projectile–target interaction, i.e. an explicit Euler method for the projectile equation and a forward (implicit) method for the target boundary value problem. At each time step, a mixed finite element and finite‐volume strategy is used to solve the ‘target’ boundary value problem. Specifically, the non‐linear variational inequality for the velocity field is discretized using the finite element method while a finite‐volume method is used for the hyperbolic mass conservation and damage evolution equations. To solve the velocity problem, a decomposition–coordination formulation coupled with the augmented Lagrangian method is adopted. Numerical simulations of penetration into concrete were performed. By conducting a time step sensitivity study, it was shown that the numerical model is robust and computationally inexpensive. For the constants involved in the model (shear and volumetric viscosities, cut‐off yield limit, and exponential weakening parameter for friction) that cannot be determined from data, a parametric study was performed. It is shown that using the material model and numerical algorithms that developed the evolution of the density changes around the penetration tunnel, the shape and location of the rigid/plastic boundary, the compaction zones, and the extent of damage due to air‐void collapse are described accurately. Copyright © 2007 John Wiley & Sons, Ltd.     

Trading reliability targets within a supply chain using Shapley's value

The development of complex systems involves a multi-tier supply chain, with each organisation allocated a reliability target for their sub-system or component part apportioned from system requirements. Agreements about targets are made early in the system lifecycle when considerable uncertainty exists about the design detail and potential failure modes. Hence resources required to achieve reliability are unpredictable. Some types of contracts provide incentives for organisations to negotiate targets so that system reliability requirements are met, but at minimum cost to the supply chain. This paper proposes a mechanism for deriving a fair price for trading reliability targets between suppliers using information gained about potential failure modes through development and the costs of activities required to generate such information. The approach is based upon Shapley's value and is illustrated through examples for a particular reliability growth model, and associated empirical cost model, developed for problems motivated by the aerospace industry. The paper aims to demonstrate the feasibility of the method and discuss how it could be extended to other reliability allocation models.     

Oblique penetration of a rigid projectile into an elastic-plastic target

The main objective of the present work is to develop an approximate solution of the problem of oblique penetration of a rigid projectile into an elastic-plastic target of finite thickness. This is accomplished by generalizing the work on normal penetration reported in [1]. Here, an irrotational isochoric velocity field is considered that consists of three parts, each of which together satisfy the condition of impenetrability at the projectile's surface. The first part is associated with the longitudinal motion of the projectile, the second part with the transverse motion, and the third part with the projectile rotation in the plane defined by the initial longitudinal projectile velocity and the normal to the target surface. The target material is assumed to be incompressible and the target region is subdivided into an elastic region ahead of the projectile, and a rigid-plastic region near the projectile. Using the above potential velocity field, inertia effects are included and the linear momentum equation is solved exactly in the elastic region. In the plastic region, the linear momentum equation is integrated numerically along the instantaneous streamlines to determine the pressure field on the projectile surface. Then the decelerating force and moment applied to the projectile are solved numerically. The model developed here predicts the residual velocity, the ballistic limit, as well as the residual angle of obliquity. Moreover, this model is able to describe the phenomenon of ricochet. It is shown that the agreement of the theory with experiments is good even though no adjustable parameters are used. Also, a user-friendly computer program has been developed that is available for distribution along with a Users' Manual.     

Mass loss from abrasion on ogive-nose steel projectiles that penetrate concrete targets

We developed an abrasion model that predicts mass loss and change in nose shape for steel projectiles that penetrate concrete targets. Mass loss data from four sets of experiments with two ogive-nose projectile geometries and concrete targets with limestone and quartz aggregates were used to develop the abrasion model. We plotted post-test mass loss versus initial kinetic energy and found a nearly linear dependence for striking velocities to approximately 1000 m/s. With this linear relationship, we derived a mathematical model that was implemented into the Sandia-developed, Eulerian hydrocode CTH. Predictions from CTH agreed well with experimental observations.     

Reliability estimates for flawed mortar projectile bodies

The Army routinely screens mortar projectiles for defects in safety-critical parts. In 2003, several lots of mortar projectiles had a relatively high defect rate, 0.24%. Before releasing the projectiles, the Army reevaluated the chance of a safety-critical failure. Limit state functions and Monte Carlo simulations were used to estimate reliability. Measured distributions of wall thickness, defect rate, material strength, and applied loads were used with calculated stresses to estimate the probability of failure. The results predicted less than one failure in one million firings. As of 2008, the mortar projectiles have been used without any safety-critical incident.     

Dynamic penetration of graphite/epoxy laminates impacted by a blunt-ended projectile

The dynamic penetration of graphite/epoxy laminates as a result of impact by a blunt-ended projectile is investigated in the present study. The ballistic limit is determined by a series of high-velocity impact tests. A dynamic finite element analysis is performed to simulate the penetration process in composite laminates. A previously developed static penetration model is incorporated into the analysis to predict the ballistic limit. The ballistic characteristics are represented by the relationship between the striking and residual velocities of the projectile. Good agreement between experimental data and computational results implies that the ballistic limit of graphite/epoxy laminates can be predicted by the present analysis without performing dynamic impact tests.     

Time-resolved penetration of long rods into steel targets

The penetration behavior of tungsten alloy, long-rod penetrators into high-hard steel is investigated at two impact velocities; 1.25 km/s and 1.70 km/s. The positions of the nose and tail of the projectile were measured by means of a 600 kV flash X-ray system at different times during penetration. The wavecode CTH was used to numerically simulate the experiments. The computational results are in very good agreement with the experimental position-time data. Additionally, the computational model reproduces the qualitative behavior for impact conditions near the ballistic limit.