Werner Goldsmith

Non-ideal projectile impact on targets

Abstract This survey summarizes analytical, numerical and experimental investigations of targets subjected to non-standard collisions, penetration and perforation of strikers, defined as all cases other than normal impingement of a purely translating impactor on a stationary target at normal incidence. The vast majority of ballistic studies are concerned with the standard configuration and conditions indicated, but virtually all field situations deviate from this scenario. The topics treated here include: oblique impact, yaw impact, impact with yaw and obliquity, impact on moving targets, rotating penetrators, impact of tumbling projectiles, impingement of jets or long rods with relative target motion, and ricochet. Other types of nonideal projectile impact exist, but have not been sufficiently explored to be documented here. The sections are divided by striker type (where applicable) as spheres, projectiles and long rods; by velocity range, and by the type of investigation performed. Sufficient technical information is presented to provide a reasonable assessment of the character, approach and results obtained for the various studies. If more detailed information concerning analytical or experimental procedures are required, the reader should consult the original references which are fully listed.

An experimental study of energy absorption in impact on sandwich plates

Summary An experimental study of the impact of blunt strikers with a diameter of 1.85 in. (47mm) on both bare honeycombs and sandwich plates with honeycomb cores is described. Both of these targets were supported by a rigid backing, whereas the latter was also examined under simply-supported conditions. The lateral extent of the samples was greater than the contact area, but the thickness of the cores was limited to 0.75 in. (19mm) and that of the sandwiches was less than 1.0 in. (25 mm). Cell dimensions and face plate thickness were substantially smaller than the striker diameter. Impact velocities, which ranged from 33 to 131 ft/s (10–40m/s) were designed to just attain densification of the targets, i.e. a condition that stopped short of further loading of the plate when complete crushing of the core had been achieved. The best correlation of energy absorption capacity without considering areal density was found to be the energy absorbed per unit of crush.

Penetration of laminated Kevlar by projectiles—I. Experimental investigation

Abstract The response of woven Kevlar/polyester laminates of varying thicknesses to quasi-static and dynamic penetration by cylindro-conical projectiles with an apex of primarily 60° has been investigated. The static properties of the material were obtained by means of standard testing procedures, including in-plane tension, compression and shear, through-thickness compression, fracture toughness and cone indentation. Compressive dynamic results were obtained using a Hopkinson bar at rates up to 2000 s−1. Quasi-static force-indentation behavior for conical indenters was determined for a specimen thickness ranging from three to 10 layers to provide constitutive relations for the corresponding analytical model. These data exhibit a linear rise whose slope and peak values are proportional to specimen stiffness, followed by a plateau that terminates in a rapid reduction to a small, but finite force level when the shank of the penetrator exits. The curves were found to be highly sensitive to the size of the projectiles and the tip angle. Static investigations were also conducted to assess the effect on penetration of specimens subject to special artificial initial conditions. This included a restraint on the global plate deformation; the use of several samples of the same total thickness, but comprised of several assemblies of stacked laminates; and embedment of an artificial dclamination flaw located centrally at the midplane of the plate over approximately half of its diameter. The dynamic tests were executed using both pneumatic and powder guns, mostly with a 12.7 mm barrel diameter. Ballistic limits were determined for these plates and terminal velocities were measured when perforation occurred. Deliberately introduced delaminations and changes in the volume fraction did not result in significant changes in the impact resistance. The damage zone created was square in shape for a 0/90 lay-up and circular for quasi-isotropic specimens. The damage pattern for dynamic loading was, however, quite different from that for the corresponding quasistatic penetration case. Kevlar laminates were found to be very resistant in arresting blunt-nosed strikers in comparison with metals on a specific weight basis.

Axial mechanical properties of fresh human cerebral blood vessels.

Human cerebral blood vessels are frequently damaged in head impact, whether accidental or deliberate, resulting in intracranial bleeding. Additionally, the vasculature constitutes the support structure for the brain and, hence, plays a key role in the cranial load response. Quantification of its mechanical behavior, including limiting loads, is thus required for a proper understanding and modeling of traumatic brain injury--as well as providing substantial assistance in the development and application of preventive measures. It is believed that axial stretching is the dominant loading mode for the blood vessels, regardless of the nature of the insult. Eighteen arteries and fourteen veins were obtained from the cortical surface of the cerebral temporal lobe of patients undergoing surgery. These vessels were stretched to failure in the longitudinal direction, either quasi-statically or dynamically. The significance of specimen and experiment parameters was determined using multivariate analysis of variance (MANOVA) testing. Results demonstrate that the arteries were considerably stiffer than the veins, carrying approximately twice as much stress at failure but withstanding only half as much stretch. No significant rate dependence was measured over a strain rate range of more than four orders of magnitude (0.01 to 500 s -1).

Response of a human head/neck/upper-torso replica to dynamic loading-II. Analytical/numerical model

A three-dimensional lumped-parameter model of the human head/neck/upper-torso was developed to predict its motion for any specified initial conditions and that could also be used to compare with the results of other investigators. This model consists of ten rigid bodies representing the head, cervical vertebrae C1-C7, T1 and T2 combined with the rest of the torso. These rigid bodies were connected by intervertebral joints described by a stiffness matrix relating the force (moment) and translation (rotation). Fifteen pairs of muscles were incorporated in the model, represented by three-point linear elements with nonlinear constitutive relationships obtained from cadaver test results. The calculated response compared favorably with human volunteer data for both flexion and lateral whiplash. However, tests on an inanimate replica of a human indicated greater flexibility than predicted by the corresponding numerical model. The difference is believed to be due to insufficient mass of the muscles incorporated in the structure.

Normal projectile penetration and perforation of layered targets

Abstract The response to normal impact of hard-steel blunt and conically-nosed projectiles on multi-layered plates of soft aluminum, both adjacent and spaced, as well as on adjacent disks of thin aluminum and polycarbonate, including sandwich arrangements, was studied experimentally in the subordnance velocity regime in the vicinity of the ballistic limit. A comparison of the penetration resistance of these targets with corresponding monolithic plates of aluminum or polycarbonate has been effected on the basis of aereal density. The ballistic resistance of the metallic monolithic target was found to be greater than that of several adjoining plates of the same thickness; this was considered to be due to the greater bending resistance of the former. On the other hand, a 15% greater ballistic resistance of the polycarbonate target was observed than for the corresponding aluminum disk. In several cases where an adjacent aluminum layer preceded the polymer, a terminal deflection of the aluminum plate in the direction opposite to that of the striker travel was observed, which was found to be due to the change in the penetration mode of the metal from petalling to extrusion. Elastic energy stored in the polycarbonate was returned to the metal cover, causing not only this rearward deflection, but also vibrations. When this occured at the ballistic limit, the period of these oscillations was found to correspond closely to that of a plate with a distributed mass with the projectile mass concentrated at its center. Wave propagation effects were not considered in the analysis, but also contribute to this reversed deflection. The experimental ballistic limits for monolithic targets of the two materials were compared to predictions of other investigators for both the blunt and conically-tipped strikers, derived from simple models of the process. The expected ballistic limit for combined targets was calculated from an energy approach with the aid of relations for this parameter based on the above models for a single material. Satisfactory correspondence was obtained between the test results and calculated values.

Penetration of laminated Kevlar by projectiles. II : Analytical model

Abstract An analytical representation of the normal impact and perforation of conically-tipped hard-steel cylinders with an aspect ratio of three on laminated Kevlar 29/poIyester targets was developed to accompany corresponding text information. The global deflection was obtained using laminated plate theory; dissipative mechanisms including indentation of the striker tip, bulging at the surface, fiber failure, delamination and friction were modeled using certain simplifying assumptions. The event was divided into three consecutive phases: indentation, perforation and exit. Resistive forces for each of these mechanisms, valid for both static and dynamic penetration, were ascertained and, for the latter case, used in conjunction with Newtons law to provide the plate response and the kinematic history of the projectile. A finite difference scheme was employed to obtain the numerical results. A comparison of the ballistic limits and of terminal velocities for higher initial speeds obtained from the model and from tests showed very good agreement. The accord between predicted and measured displacement histories is satisfactory, but deteriorates successively when velocities and accelerations are examined. This effect is due to the process of differentiation of data as well as inaccuracies in the analytical representation. Methods for extending the model arc suggested.

Plastic deformation and perforation of thin plates resulting from projectile impact

Abstract The dynamic response of thin plates subjected to projectile impact was studied experimentally by measuring projectile velocity, permanent deformation, dynamic strain and displacements and by examining the growth of plastic deformation and motion of the projectile with a high speed framing camera. Most of the experimental work was performed with ½ in. diameter steel projectiles, spherical or cylindro-conical in shape, centrally striking a 2024-0 aluminum plate, 0.050 in. thick and clamped on a 14 ½ in. diameter, at normal velocities ranging from 75 to 933 ft/sec. Projectile speeds were chosen so as to produce significant plastic deformation at the lower velocities and complete perforation at the higher velocities. The circular boundary of the plastic zone was found to propagate away from the point of impact at about 8800 in./sec at all impact velocities. A simplified large deflection solution for the final central deflection of a rigid/plastic linearly work-hardening plate showed good agreement with the data and correlation between various perforation theories and experimental data was found to improve with increasing projectile velocity.

Quasi-static and ballistic perforation of carbon fiber laminates

Abstract The partial and complete perforation of woven carbon fiber/epoxy laminates with thicknesses ranging from 1.3 to 6.6 mm by 60° cylindro-conical hard steel strikers at normal incidence has been examined under both quasi-static and dynamic conditions. Quasi-static experiments were conducted in a standard experiments were conducted in a standard testing machine at rates ranging from 0.012 to 6.5 s −1 , where the load-deflection was obtained. Ballistic projectile with an aspect ratio of three fired from either a compressed gas or a powder gun at speeds varying from 30 to 310 m/s, with the initial and final velocity (when present) of the striker always measured, in addition to selected high-speed photographic recording. The damaged samples were carefully examined with respect to failure modes. Major mechanisms of the deformation and damage processes were modelled on the basis of energy absorption, including global plate deflection, fiber, breakage, delamination and bending of petals, hole enlargement and friction between striker and sample. For the dynamic case, the predictions were 70–96% of the observed expenditure level. This is considered to be due to the absence in the analysis of factors such as inertia, strain-rate and wave propagation effects, matrix shearing and fragmentation, as well as obliquity and rotation motion of the striker. The correspondence in the case of static loading was considerably poorer, indicating substantial and non-measurable energy absorption by the test apparatus, including substantial frictional dissipation in in the specimen holder and between sample and penetrator.

Petalling of thin, metallic plates during penetration by cylindro-conical projectiles

Abstract A theoretical and experimental investigation has been undertaken to study the processes of perforation at normal incidence of thin, soft aluminum plates by hard-steel cylindroconical projectiles of 30° half-cone angle. The analysis is executed by means of an energy balance for a rigid/perfectly-plastic or work-hardening material. For an intact plate, where petalling always occurs, consecutive stages of the process involve initial crack propagation followed by plastic hinge motion out to the position of crack arrest, followed by petal bending due to hinge rotation up to and beyond the point of projectile passage. In the case of central impact on an initial hole in the plate, the first stage constitutes an enlargement of the hole, followed by crack propagation and bending of trapezoidal regions of the plate until the projectile has either perforated or is embedded in the target. Tests conducted on 2024-0 aluminum with a thickness of 3.175 mm indicated a condition so that if the initial hole radius was greater than about 2/3 that of the 12.7 mm diameter hard-steel projectile, cracking did not occur and all the energy was absorbed by hole enlargement. Furthermore, for each initial impact velocity, an optimal hole radius was found to exist where a maximum energy absorption of the plate occurred, greater than for the intact target. This phenomenon was qualitatively substantiated by the theory; discrepancies in magnitudes are attributed to the neglect of certain energies in the analysis, particularly that of dishing. Excellent correlation was found between the theoretical prediction for the terminal velocity of a projectile striking the intact plate and test results when an estimate of the dishing energy for the plate was included.