Impact behaviour of PELE projectiles perforating thin target plates

The first experiments with a penetrator with enhanced lateral efficiency (PELE) were carried out in 1996. The unusual behaviour of the penetrator as it perforates a target can generally be described in three main stages. In the first stage the different kinetic energies of the jacket and the filling lead to the enclosure of the filling material. This induces a pressure rise in the filling, which dilates the surrounding jacket in the second stage. During the last stage the high-density jacket breaks into pieces. When a thin target, as in our case, is perforated, a fourth stage must be added to the other three. This new stage describes the interaction between the filling and the plug, which is produced during the impact. For the lateral efficiency of the PELE, the second stage is the important one. The behaviour in this stage (pressure build-up and radial expansion of the jacket) is dominated by only a few physical parameters. For weak shock waves, these parameters are determined by theoretical consideration. A number of experiments were carried out in the velocity range between 900 and 3000 m/s in order to obtain an experimental database. In the last section a comparison between the physical model and experimental data gives a short outline of the complex impact behaviour of the PELE projectile. The physical model and the experimental data are in good agreement for impact velocities under 1400 m/s. For higher velocities causing stronger shock waves, the theory has to be modified; but the set of physical parameters influencing the terminal ballistic behaviour of PELE remains valid.     

Impact analysis of laminated composite plates and shells by super finite elements

A super finite element method that exhibits coarse-mesh accuracy is used to predict the transient response of laminated composite plates and cylindrical shells subjected to non-penetrating impact by projectiles. The governing equations are based on the classical theories of thin laminated plates and shells taking into account the von Karman kinematics assumptions for moderately large deflections. A non-linear Hertzian-type contact law accounting for curvatures of the colliding bodies is adopted to calculate the impact force . The theoretical basis of the present finite element model is verified by analysing impact-loaded laminated composite plate and shell structures that have previously been studied through analytical or other numerical procedures. The predictive capability of the present numerical approach is successfully demonstrated through comparisons between experimentally-measured and computed force-time histories for impact of carbon fibre-reinforced plastic (CFRP) plates. The current computational model offers a relatively simple and efficient means of predicting the structural impact response of laminated composite plates and shells.     

A review of meshless methods for laminated and functionally graded plates and shells

This review focuses mainly on the developments of element-free or meshless methods and their applications in the analysis of composite structures. This review is organized as follows: a brief introduction to shear deformation plate and shell theories for composite structures, covering the first-order and higher-order theories, is given in Section 2. A review of meshless methods is provided in Section 3, with main emphasis on the element-free Galerkin method and reproducing kernel particle method. The applications of meshless methods in the analysis of composite structures are discussed in Section 4, including static and dynamic analysis, free vibration, buckling, and non-linear analysis. Finally, the problems and difficulties in meshless methods and possible future research directions are addressed in Section 5.     

Dynamic perforation of viscoplastic plates by rigid projectiles

A model is formulated for the dynamic perforation of viscoplastic plates by rigid projectiles. The process is considered to occur in 5 continuously coupled but distinct stages which are amenable to analytical treatment. An essential feature of the analysis is the use of postulated, physically motivated, deformation mechanisms in conjunction with the upper bound theorem of plasticity theory which is modified to include dynamic effects. Special attention is given to the bulging process and effects associated with the later stages. This model is self-contained and capable of predicting the exit velocities of the projectile and the plug. It also determines the bulge and plug shape, provides the force-time history of the process, and describes a number of geometrical features of the transient and final deformation state of the target plate.     

Yawing impact on thin plates by blunt projectiles

Two experimental investigations and a corresponding analytical study were conducted to examine the phenomena attendant to the impact of blunt-nosed, hard-steel strikers on stationary thin plates of aluminum and steel at moderate angles of yaw and zero obliquity. The variation of ballistic limit with yaw angle or the terminal velocity and final trajectory angle in perforation tests were ascertained. Post-mortem examination of the plates indicated that damage and failure occurred by bulging, lateral indentation, and side and front petaling. A theoretical model based on a membrane representation was developed that analyzed the impact by dividing the process into five stages. This model underpredicted the ballistic limit by up to 14%, with better correlation found at higher yaw angles. Excellent agreement was observed between the experimental and analytical final velocities when the data points were corrected to reflect the difference between the experimental values of the ballistic limit and that predicted by the model. Fair agreement was found between the experimental and the analytical values of the trajectory angle.     

Impact of thick PMMA plates by long projectiles at low velocities. Part II: Effect of confinement

A hybrid experimental–numerical investigation of the penetration process in unconfined and confined thick polymethylmethacrylate (PMMA) plates was carried out. The confinement was applied by insertion of the polymeric plate into a conical steel ring. The response of such plates to the impact of long hard steel projectiles having an ogive-head shape in the range of velocities of 165 < V₀ < 260 (m/s), was investigated experimentally. The results show that unconfined targets were perforated and broken due to combined effect of penetration and cracking. By contrast, the confined targets were not perforated and could withstand repeated impacts due to suppression of the brittle damage mechanism by the confinement. The tests were modeled using 3D explicit finite element analyses. A good agreement regarding the trajectory of the projectile and the depths of penetration was obtained. The numerical results show that the confinement introduces a negative triaxiality and even some plasticity within the confined plates prior to impact. The increase of plastic failure strain of the PMMA at negative triaxiality reduces the ductile damage during penetration, while the hydrostatic pressure reduces significantly the brittle fracture mechanism. The resisting force to the penetration depends on the failure strain–triaxality relationship, and does not necessarily increase with higher confinement levels.     

Impact loading of plates — An experimental investigation

The impact of projectiles at sub-ordnance velocities against mild steel, stainless steel and aluminium plates, has been studied in a series of experiments. The projectile mass, nose shape and hardness have been shown to have an important effect on penetration as does the target rigidity and support condition. All materials exhibit a clear ‘kink’ effect related to a change from energy absorption by plastic deformation to perforation with well-defined shear bands and no appreciable bulging.     

Ultimate load behaviour of reinforced concrete plates and shells under dynamic transient loading

This paper considers a layered thick shell finite element procedure for determining the dynamic transient nonlinear response of plates and shells. The degenerated three-dimensional isoparametric shell element with independent rotational and translational degrees-of-freedom is employed and a layered formulation is adopted to represent the steel reinforcement and to simulate progressive concrete cracking through the thickness. The dynamic yielding function is assumed to be a function of the current strain rate, in addition to being total plastic strain or work dependent. The concrete model also simulates both compressive crushing and tensile cracking behaviours and an implicit Newmark algorithm is employed for time integration of the equations of motion. Several numerical examples are presented for both slab and shell structures and the results obtained compared with those from other sources wherever available.     

Elasticity and viscoelasticity in layered shells and plates subject to thermal and force loading

A revised model has been devised for the thermoelastic equilibrium in a multilayer shell of rotation that incorporates the thermal sensitivity of the material and the variable layer thicknesses, as well as the temperature dependence of the transverse tangential stress distribution. The linear theory of inherited elasticity is employed to derive differential equations for the quasistatic equilibrium of a multilayer viscoelastic shell or plate made from thermorheologically complicated materials. The solution is obtained as double trigonometric series for a hinge-supporied viscoelastic cylindrical shell or plate subject to sinusoidal temperature and force loadings.Translated from Problemy Prochnosti, Nos. 5–6, pp. 95–103, May–June, 1995.     

Impact fragmentation of high-velocity compact projectiles on thin plates: a physical and statistical characterization of fragment debris

The high-velocity impact of a projectile onto a structure results in the creation and energetic expulsion of fragments of the interacting materials. The nature of this fragment debris is of concern in certain applications. Although more broadly applicable, the present study is motivated by a need to characterize the size and velocity distribution of fragments generated by orbital debris impacting external components of spacecraft structure, such as shielding and radiators. In this effort, statistical relations are developed to predict size, momentum and trajectory distributions of the debris. The underlying physics applied are those used in the fields of impact mechanics, thermodynamics of shocks, and statistical fragmentation. Equations from impact mechanics lead to predictions for mass, global momentum, and excess energy of the fragment debris. Relations from shock thermodynamics are developed to partition the initial kinetic energy into thermal and mechanical energies, and therefore to predict mass fractions of solid, liquid and vapor components and the subsequent dispersing motion of this fragment debris. Statistical methods of the energy-based Maxwell-Boltzmann type are pursued to characterize the inherently stochastic fragmentation event, emphasizing the extremes of fragment size and velocity. Computational simulations of impact events and data from impact fragmentation experiments are exploited in validating the underlying theoretical assumptions and the resulting impact fragmentation model.     

Experimental investigation into scaling laws for conical shells struck by projectiles

An experimental investigation is reported into the scaling laws for fully clamped thin-walled mild steel conical shells struck axially by plane-head cylindrical projectiles travelling at velocities between 29.5 and 54 m/s. The test shells and projectiles have scale factors of 1, 2 and 4. Some tests are conducted to determine the critical impact velocities to cause cracking or perforation. The other tests are conducted with impact energies which produce dynamic plastic buckling without any rupture or cracking. The critical velocities and the permanent axial deflections of the shells do not obey the elementary geometrically similar scaling laws. The larger deviations are related with the higher impact velocities and larger scale factors. The material strain rate sensitivity effects may be the main factor causing the deviations. The other factor is the localization of the deformation during dynamic plastic buckling.     

Ricochet of deforming projectiles from deforming plates

Ricochet means rebound of a striker from the impacted surface (or penetration into a medium along a curved trajectory emerging through the impacted surface with a residual velocity). Changes in direction, velocity and rotational motion of the penetrator are due to several mechanisms. These include release of stored elastic impact energy; influence of surfaces, material interfaces and impact deformations in the target on the magnitude and direction of the resisting force during impact; resistance to motion due to drag and friction. The subject is of interest due to the need to establish safety zones and to design containment structures to guard against failure of rapidly moving machine parts, to protect outer components of space vehicles from the energetic debris spray resulting from oblique hypervelocity impact and to reconstruct bullet trajectories in forensic engineering. This paper contrasts two-dimensional plane strain calculations of ricochet with fully three-dimensional simulations performed with Apollo, a three-dimensional Lagrangian finite element code for impact and explosive loading problems set up exclusively on personal computers and workstations. While some useful information can be extracted from plane strain calculations regarding the early stages of impact, the use of two-dimensional calculations to simulate fully three-dimensional phenomena with long response times (up to the millisecond regime) results in gross overestimation of deflections and is inherently dangerous.     

Direct force measurement in normal and oblique impact of plates by projectiles

An experimental investigation of the forces produced by the penetration and perforation of thin aluminum and steel plates by cylindro-conical and hemispherically-tipped projectiles at 0, 15, 30 and 45° angles of incidence has been performed. Additionally, force histories were recorded for normal impact on Lexan, nylon and ceramic targets by conically-tipped strikers. Similar tests on Kevlar were not successful owing to the generation of voltages by rubbing of fibers that completely overwhelmed the transducer signal. A piezoelectric crystal bonded to the tail of the 12.7 mm diameter, 30 g projectiles followed by an inertial mass and a trailing wire provided the instrumentation. The strikers were propelled by means of a pneumatic gun at velocities ranging from 45 to 170 ms⁻¹. Displacement data obtained from high-speed photography for selected runs allowed curve fits to an analytical function which were compared to the directly recorded force histories.The effects of changes in initial velocity, angle of obliquity and striker tip on the peak force have been analyzed. A simple model has been developed for the perforation of plates by hemispherically-tipped projectiles at oblique incidence, and comparisons have been made with the measured force histories. A model was also devised to predict the peak forces obtained for oblique impact by cylindro-conical projectiles. The peak forces obtained experimentally were found to be relatively independent of the initial projectile velocity for shots where perforation occured. For the tests at speeds below the ballistic limit, the maximum forces were approximately proportional to the initial velocity.     

A triangular finite element for thin plates and shells

A finite element modelling technique which utilizes a triangular element with 45 degrees-of-freedom and seven-point integration has been tested for analysis of thin plate and shell structures. The element is based on the degenerate solid shell concept and the mixed formulation with assumed independent inplane and transverse shear strains. Numerical result indicates effectiveness of the present modelling technique which features combined use of elements with kinematic modes and those without kinematic modes in an attempt to eliminate both locking and spurious kinematic modes at global structural level.     

Impact deformation of polymeric projectiles

Post-impact deformation of projectiles is studied in relation to flyer-plate thickness and standoff distance from a rigid anvil, without significant penetration and perforation of the flyer plate. A close-range photogrammetric measuring technique is used to determine the final profiles of polymeric cylindrical projectiles. This non-destructive measurement technique is utilized to study the effects of projectile nose geometry on the high rate deformation process, at speeds ranging from 100 to 600 m/s, in connection with metal sheet deformation during impact spot welding. An Imacon ultra-high speed camera is used to photograph the deforming polymeric projectiles.     

Comparative analysis of perforation models of metallic plates by rigid sharp-nosed projectiles

Based on the mode of ductile hole enlargement, the present paper compares the models of a rigid sharp-nosed projectile perforating the ductile metallic target plate, given by Chen and Li [1] and Forrestal and Warren [2], respectively. It indicates that the formulae of ballistic limit and residual velocity of these two perforation models are consistent in form but with different applicable range, which due to them employing the spherical cavity expansion theory and cylindrical cavity expansion theory, alternately. Further analyses are conducted to discuss the effects of target material and plate thickness on the terminal ballistic performance with referring the experimental results of aluminum alloy and Weldox E steel plates. It is confirmed that the perforation mechanisms may transform with increasing the plate thickness and the strength of target material.     

Effect of thin oblique moving plates on long rod projectiles: A reverse impact study

The geometry and motion of long rod projectiles after penetrating thin obliquely oriented and moving armour plates were studied. Plates moving in their normal directions towards as well as away from the projectile (scalar product of velocities negative and positive, respectively) were considered. The influences of plate velocity and obliquity (angle between the normal of the plate and the axis of the projectile) were investigated through small-scale reverse impact tests with tungsten projectiles of length 30 mm and diameter 2 mm, and with 2 mm-thick steel plates. The obliquity (30°, 60° and 70°) and the plate velocity (300 to −300 m/s) were varied systematically for a projectile velocity of 2000 m/s. The disturbing effect of the plate on the projectile was characterised in terms of changes in length, velocity, angular momentum, linear momentum and kinetic energy. Plates with obliquity 60–70° moving away from the projectiles with velocity 200–300 m/s were found to cause extensive fragmentation of the projectile and to have large disturbing effects in terms of all measures used.