David L. Littlefield

Long-rod penetration, target resistance, and hypervelocity impact

Abstract Numerical simulations are used to examine long-rod penetration as a function of impact velocity. Similarities and differences between the penetration histories are analyzed, including penetration and tail velocities, penetration depths, crater radii, centerline interfaces pressures, and the extents of plastic flow in the projectile and target. The one-dimensional modified Bernoulli theory is often used to examine long-rod penetration into semi-infinite targets, and integral to the theory is a term that describes the resistance of the target to penetration. It is observed that the target resistance decreases with impact velocity, and it is shown that this is a consequence of both the residual phase of penetration and variations in the size of the plastic zone field.

The effect of electromagnetic fields on the stability of a uniformly elongating plastic jet

In this paper the stability characteristics of an infinitely long, uniformly elongating metal jet are investigated. The application to a metallic jet formed from an explosive charge, or shaped‐charge jet, is of particular interest. The effect of an axial electric current on the stability of the jet is determined. The jet is assumed to be perfectly plastic, perfectly conducting, nonswirling, and isothermal. The governing equations are solved to determine the idealized motion of the jet, which is then perturbed by an arbitrary three‐dimensional disturbance. The resulting first‐order equations are solved numerically for the time evolution of this perturbation. For a given initial condition, the growth rate of the disturbance depends on the relative importance of the inertial, electrical, and plastic forces. The details of growth rate characteristics are explained in terms of the appropriate physical principles.

The penetration of steel targets finite in radial extent

An experimental, analytical, and computational effort was undertaken to examine the effect of confinement on penetration in armor-like steel targets. For the experiments, LD 10, tungsten-alloy projectiles were fired at 1.5 km/s into 4340 steel cylindrical rounds of various diameters. Penetration efficiencies, as measured by the depth of penetration normalized by the original projectile length (PL), were determined and the results plotted as a function of normalized target diameter DtD, where Dt is the target diameter and D is the projectile diameter. As DtD changed from 20 to 5, PL increased by 28%, although PL was approximately independent of DtD for DtD ⪆ 15. An analytical model using a modified cavity expansion theory was developed to estimate the resistance to penetration for targets of finite lateral extent. The analytical model shows decreasing target resistance as DtD decreases below approximately 30; in particular, target resistance decreases rapidly for DtD < 20. Numerical simulations were performed and the computational predictions are in excellent agreement with the experimental results; simulations were used to extend DtD between 3 and 78. Plastic strain contours are plotted to assess the extent of plastic flow within the target; the results of the simulations demonstrate that PL begins to increase when the extent of plastic flow in the target reaches the radial boundary.

Thermomechanical and magnetohydrodynamic stability of elongating plastic jets

In this study the stability characteristics of uniformly elongating plastic jets exposed to axial electric currents are investigated. The objective of this study is to expand the results of previous analyses by Littlefield [‘‘The effect of electromagnetic fields on the stability of a uniformly elongating plastic jet,’’ Phys. Fluids A 2, 2240 (1990); ‘‘Finite conductivity effects on the MHD instabilities in uniformly elongating plastic jets,’’ ibid. 3, 166 (1991); ‘‘Enhancement of stability in uniformly elongating plastic jets with electromagnetic fields,’’ ibid. 3, 2927 (1991)] to include high levels of electric current, where thermal energy effects must be included. Coupling of the magnetohydrodynamic and thermal characteristics of the flow is accomplished through the variation of mechanical, thermal, and electrical properties with temperature. Phase change effects are also considered. The jet is assumed incompressible and perfectly plastic, with the Levy–von Mises criterion imposed to limit the effectiv...

Finite conductivity effects on the MHD instabilities in uniformly elongating plastic jets

The effect of finite electrical conductivity on the stability of perfectly plastic jets is considered. Application of the analysis to shaped‐charge jets is of primary interest. The jet is assumed to be uniformly elongating and axisymmetric. An axial electric current is introduced in the jet at time t=0 and permitted to diffuse over time. After base solutions to the relevant governing equations are calculated, the stability characteristics of the jet are determined using linear perturbation theory. Solutions to the first‐order equations indicate that disturbances in the magnetic field and pressure distributions vary significantly depending on the conductivity. The growth rate in the boundary perturbation, however, demonstrates that jets of finite conductivity are only slightly more stable than equivalent jets of infinite conductivity. The behavior of these instabilities is discussed in terms of the applicable physical mechanisms.

Dependence of debris cloud formation on projectile shape

A two‐stage lights‐gas gun has been used to impact thin zinc bumpers by zinc projectiles over the velocity range of 2.4 km/s to 6.7 km/s to determine the propagation characteristics of the impact generated debris. Constant‐mass projectiles in the form of spheres, discs, cylinders, and rods were used in these studies. Radiographic techniques were employed to record the debris cloud generated upon impact and the dynamic formation of the resulting rupture in an aluminum backing plate resulting from the loading of the debris cloud. The characteristics of the debris cloud generated upon impact is found to depend on the projectile shape. The data indicate that the debris front velocity is independent of the shape of the projectile, whereas the debris lateral/radial velocity is strongly dependent on projectile geometry. Spherical impactors generate the most radially dispersed debris cloud while the normal plate impactors result in column‐like debris. It has been observed that the debris generated by the impact o...

Validation and calibration of a lateral confinement model for long-rod penetration at ordnance and high velocities

In designing targets for laboratory long-rod penetration tests, the question of lateral confinement often arises, “How wide should the target be to exert enough confinement?” For ceramic targets, the problem is enhanced as ceramics are usually weak in tension and therefore have less self-confinement capability. At high velocities the problem is enhanced even more as the crater radius and the extent of the plastic zone around it are larger. Recently we used the quasistatic cavity expansion model to estimate the resistance of ceramic targets and its dependence on impact velocity [1]. We validated the model by comparing it to computer simulations in which we used the same strength model. Here we use the same approach to address the problem of lateral confinement. We solved the quasistatic cavity expansion problem in a cylinder with a finite outside radius “b” at which σr (b) = 0 (σr = radial stress component). We did this for three cases: ceramic targets, metal targets, and ceramic targets confined in a metal casing. Generally, σr (a) is a decreasing function of “a” (“a” = expanding cavity radius, and σr (a) = the stress needed to continue opening the cavity). In the usual cavity expansion problem b → ∞, σr (a) = const., R =−σr (a) (R = resistance to penetration). For finite “b” we estimate R by averaging σr (a) over a range o ≤ a ≤ ar, (where ar, the upper bound of the range, is calibrated from computer simulations). We ran 14 computer simulations with the CTH wavecode and used the results to calibrate ar for the different cases and to establish the overall validity of our approach. We show that generally for DtDp > 30, the degree of confinement is higher than 95% (Dt = target diameter; Dp = projectile diameter; and degree of confinement = RR∞; R∞ = resistance of a laterally infinite target). We also show the tensile strength of ceramic targets (represented by the spall strength Pmin) has a significant effect on the degree of confinement, while other material parameters have only a minor effect.

A Probabilistic Approach to Aircraft Turbine Rotor Material Design

A probabilistic design code is being developed for high energy disks and rotors used in aircraft gas turbine engines. This code is intended to augment, not replace, the current safe-life approach to the design of these critical components. While the code will ultimately be applicable to a range of disk alloys, initial emphasis has been placed on titanium alloys containing hard alpha defects. The approach involves developing an enhanced defect distribution for hard alpha, obtaining crack initiation data for hard alpha and fatigue crack growth data for three titanium alloys, and integrating this information into a software code that is sufficiently efficient that it can be routinely used for design and life prediction.Copyright

Enhancement of stability in uniformly elongating plastic jets with electromagnetic fields

The stability of rapidly stretching, perfectly plastic jets when subjected to axial magnetic fields is studied in this analysis. The jet is assumed to be uniformly elongating, infinitely long, and isothermal. An axial magnetic field, assumed to be provided by a solenoid in the surrounding vacuum, is initiated at time t=0. Linear perturbation theory is employed to calculate the time evolution of small disturbances in the jet. Results of the calculations indicate that imposed axial magnetic fields inhibit the growth rates of instabilities in the jet. Entrained magnetic fields, however, are present after the jet leaves the solenoid, and increase the growth rates of disturbances. As a consequence, the overall growth rates are strongly dependent on the magnetic Reynolds number. This result is explained in terms of the applicable magnetohydrodynamic (MHD) stability mechanisms in the jet.

Computational simulations of experimental impact data obtained at 7 to 11 km/s with aluminum and zinc

A combined experimental/computational program was conducted to asses the physical characteristics of impacts at speeds above those attainable using conventional light‐gas guns, but within the realm of impact encounters in space, where velocities can range from 7 to 15 km/s. A major goal of the program was to assess the capability of state‐of‐the‐art hydrocodes to reproduce damage and loading characteristics seen in hypervelocity impacts that produce diffuse molten or vaporous debris clouds. In this study the Eulerian hydrocode CTH was used. Comparisons have been made to experiments conducted with aluminium projectiles traveling from 7.4 to 11.4 km/s. A three‐stage light‐gas gun launcher was used to launch 17×1 mm aluminum disks, and an inhibited shaped charge launcher was used to launch 20×5 mm aluminum rods. Additional experiments were conducted at velocites from 3.5 to 6.6 km/s using zinc. In that range, scale modeling analysis predicts that a response similar to aluminum impacting at roughly twice the ...