The mechanics of penetration of projectiles into targets

Backman, Marvin E.; Goldsmith, Werner

doi:10.1016/0020-7225(78)90002-2

Cited by 728 publications

(288 citation statements)

References 72 publications

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“…This is similar to the Poncelet force law, F 0 + cv 2 , used in high-speed ballistics 11,12 , but accounts for the depth-dependence of Coulomb friction in granular media. Tsimring and Volfson argued that the form of F(z) should vary from quadratic to constant owing to the shapes of the projectile and of the growing crater excavated by its motion.…”

mentioning

confidence: 73%

Unified force law for granular impact cratering

2007

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Experiments on the low-speed impact of solid objects into granular media have been used both to mimic geophysical events 1-5 and to probe the unusual nature of the granular state of matter [6][7][8][9][10] . Observations have been interpreted in terms of conflicting stopping forces: product of powers of projectile depth and speed 6 ; linear in speed 7 ; constant, proportional to the initial impact speed 8 ; and proportional to depth 9,10 . This is reminiscent of high-speed ballistics impact in the nineteenth and twentieth centuries, when a plethora of empirical rules were proposed 11,12 . To make progress, we developed a means to measure projectile dynamics with 100 nm and 20 μs precision. For a 1-inch-diameter steel sphere dropped from a wide range of heights into noncohesive glass beads, we reproduce previous observations 6-10 either as reasonable approximations or as limiting behaviours. Furthermore, we demonstrate that the interaction between the projectile and the medium can be decomposed into the sum of velocity-dependent inertial drag plus depth-dependent friction. Thus, we achieve a unified description of low-speed impact phenomena and show that the complex response of granular materials to impact, although fundamentally different from that of liquids and solids, can be simply understood.To measure dynamics, we use a line-scan digital CCD (chargecoupled device) camera to image a finely striped transparent rod attached vertically to the top of the projectile (see the Methods section). The instantaneous speed is the key quantity, deduced from the displacement of the striped pattern between successive frames. The temporal precision is 20 μs, set by the 50 kHz frame rate of the line-scan camera. The position resolution is 100 nm, set by the 3.8 μm per pixel magnification divided by the square root of the number of pixels. These combine to give a velocity resolution of 0.5 cm s −1 . Besides measurement fidelity, another advantage of our method is that it applies even to very deep impacts-as long as the striped rod does not submerge.Our complete dynamics data set is shown in Fig. 1, which shows position z, velocity v, and acceleration a, versus time t, for initial impact speeds, v 0 , ranging from 0 to −400 cm s −1 . Time is measured from initial impact; position is measured upwards from the granular surface, opposite to gravity. A striking feature is that, although the final position is approached smoothly, the velocity vanishes abruptly with a discontinuity in acceleration. Similar behaviour is evident in data from an embedded accelerometer (P. B. Umbanhowar, private communication, 2004; J. C. Amato, private communication, 2005). This is counter to the viscous approach to a stable equilibrium, where acceleration vanishes continuously, but it permits the stopping time, t stop , to be easily gauged from the velocity versus time data. Note that t stop actually decreases with increasing impact speed; surprisingly, deeper penetration requires less time. Evidently, granular matter is very different from ordinary ...

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confidence: 73%

Unified force law for granular impact cratering

2007

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“…The projectile pushes the STFs with high viscosity to move ahead and act on the rear face sheet, which can be considered as a concentrated load exerted on rear face sheet. If the rear face sheet is 0.2 mm thick, it is easily deformed into a dish with tensile stress in the radial and circumferential directions [25], and then develops into petal failure mode, as shown in Fig. 6 (a).…”

Section: 3deformation Mechanismmentioning

confidence: 99%

Dynamic response of symmetrical and asymmetrical sandwich plates with shear thickening fluid core subjected to penetration loading

Tan

Zuo

et al. 2016

Materials & Design

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. (2016). Dynamic response of symmetrical and asymmetrical sandwich plates with shear thickening fluid core subjected to penetration loading. Materials and Design,[94][95][96][97][98][99][100][101][102][103][104][105][106][107][108][109][110] Dynamic response of symmetrical and asymmetrical sandwich plates with shear thickening fluid core subjected to penetration loading AbstractSymmetrical and asymmetrical sandwich plates with a shear thickening fluid (STF) core were designed to be penetrated by a cylindrical projectile at various impact velocities. These STFs consist of SiO2/PEG400, and the volume fractions of SiO2 nano-particles are 54% and 56%, respectively. Failure mode of the rear face sheet of the symmetrical sandwich plate is petal perforation, but the rear face sheet of the asymmetrical sandwich plate failed in plug perforation mode at the velocity of less than 80 m/s and in the petal perforation mode at the velocity faster than 90 m/s. The results showed that both the face sheet and the STF core played different roles in impact resisting properties and energy absorption of the sandwich plate at different impact velocities. The thickness of the rear sheet has a significant influence on the energy absorption at low impact velocity, while this influence can be ignored at high impact velocity. The effects of the particle volume fraction, impact velocity and thickness of rear face sheet on the deformation mechanism and energy absorption of the sandwich plate were also discussed. Abstract: Symmetrical and asymmetrical sandwich plates with a shear thickening fluid (STF) core were designed to be penetrated by a cylindrical projectile at various impact velocities. These STFs consist of SiO 2 /PEG400, and the volume fractions of SiO 2 nano-particles are 54% and 56%, respectively. Failure mode of the rear face sheet of the symmetrical sandwich plate is petal perforation, but the rear face sheet of the asymmetrical sandwich plate failed in plug perforation mode at the velocity of less than 80 m/s and in the petal perforation mode at the velocity faster than 90 m/s. The results showed both the face sheet and the STF core played different roles in impact resisting properties and energy absorption of the sandwich plate at different impact velocities. The thickness of the rear sheet has a significant influence on the energy absorption at low impact velocity, while this influence can be ignored at high impact velocity. The effects of the particle volume fraction, impact velocity and thickness of rear face sheet on the deformation mechanism and energy absorption of the sandwich plate were also discussed. Disciplines Engineering | Science and Technology Studies

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“…They are also seen in some types of frictional interfaces, such as impact abrasion. In ballistics, shear bands may be seen in both the penetrator and the target (Backman & Goldsmith 1978;Meunier et al 1992; Corbett et al. 1996).…”

Section: Adiabatic Shear Occurrencementioning

confidence: 99%

High-Rate Shear Deformation and Failure in Structural Alloys

Dawson¹

2002

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Experiments were conducted to determine the dynamic shear behavior of a wide range of aluminum, titanium, and steel alloys. Principal experimental techniques were the torsional Kolsky bar and the Shear Compression Specimen (SCS) geometry. For the purpose of determining adiabatic shear susceptibility in this range of alloys, it was found that both techniques were unable to induce adiabatic shear in alloys resistant to that failure mode. The SCS geometry has demonstrated a capability for characterizing shear deformation behavior over a wide range of strain rates. For modeling and simulation of adiabatic shear phenomena, an improved adiabatic temperature evolution equation has been implemented. Finite element simulations of the torsional Kolsky and SCS geometries were conducted to evaluate the influence of pre-existing geometric inhomogeneities on adiabatic shear band initiation. 3

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The mechanics of penetration of projectiles into targets

Cited by 728 publications

References 72 publications

Unified force law for granular impact cratering

Unified force law for granular impact cratering

Dynamic response of symmetrical and asymmetrical sandwich plates with shear thickening fluid core subjected to penetration loading

High-Rate Shear Deformation and Failure in Structural Alloys

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