Charles E. Anderson

An overview of the theory of hydrocodes

Abstract Hydrocodes are large computer programs that can be used to simulate numerically highly dynamic events, particularly those which include shocks. Lagrangian and Eulerian descriptions are reviewed, and advantages and disadvantages are summarized. The question of how to best represent the continuum equations on a finite computer is answered by summarizing the topics of accuracy and stability. The concept of artificial viscosity is introduced to permit the continuum code to deal with the discontinuities of shocks. Finally, a review of the treatment of materials, i.e., equation of state and constitutive response, including failure, is presented.

Ballistic impact: The status of analytical and numerical modeling

Abstract Simulation of ballistic impact generally falls into one of two categories: analytical models which assume certain dominant physical phenomena and numerical simulations, where the general continuum conservation equations are integrated in time at all points in a spatial mesh to obtain the spatial time history of stresses, strains, velocities, etc., in the projectile and target. Analytical formulations model the mechanical processes over the full field of influence which leads to approximate conservation equations for the entire region in an impact event. These for mulations have met with considerable success so long as the assumptions inherent in the model are applicable. Numerical simulations (hydrocodes) compute the wave (shock) interactions important at early times. Mechanical effects, e.g. plugging, erosion, etc., require realistic constitutive modeling which includes failure criteria and failure propagation. This paper gives a broad overview of both analytical and hydrocode modeling and examines the technical issues, uncertainties and potential diffuculties for advancement in predictive capability.

A TIME-DEPENDENT MODEL FOR LONG-ROD PENETRATION*

Abstract The one-dimensional, quasi-steady-state, modified Bernoulli theory of Tate [ J. Mech. Phys. Solids , 15 , 287 (1967)] is often used to examine long-rod penetration into semi-infinite targets. In general., the time histories of penetration predicted by the Tate model can be in good agreement with those computed from numerical simulations. However, discrepancies exist between the model and numerical simulations at the beginning and at the end of penetration. From insights provided by numerical simulations, assumptions are made concerning the velocity and stress profiles in the projectile and the target. Using these assumptions, the time-dependent, cylindrically-symmetric, axial momentum equation is explicitly integrated along the centerline of the projectile and target to provide the equation of motion. The model requires the initial interface velocity—which can be found, for example, from the shock jump conditions-and material properties of the projectile and target to compute the time history of penetration. Agreement between the predictions of this one-dimensional, time-dependent penetration model are in good agreement with experimental results and numerical simulations.

A thermodynamic heat transfer model for intumescent systems

Abstract A mathematical model has been developed which describes the various physical processes of an intumescent system by considering mass and energy control volumes. Expansion is explicitly accounted for by assuming it to be a function of mass loss. Thermodynamic data from thermogravimetric analysis and differential scanning calorimeter characterizes the chemical constituents of the coating. A computer program has been written to solve the system of equations, with appropriate boundary conditions, as a function of time. Model predictions are compared against experimental data.

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.

Time-resolved penetration of long rods into steel targets

Abstract 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.

Debris cloud dynamics

Abstract The hypervelocity impact of a projectile upon a thin metal plate and subsequent formation of back-surface debris is reviewed. At sufficiently high impact velocities, roughly greater than 3.0 km/s (depending upon the shock impedances of the materials involved), shock formation and interaction dominate and control the overall response of both the projectile and the target plate. We focus upon the importance of shock heating, melting, and vaporization in this application. Because of the complexity of the physical interactions, numerical simulation of such problems is necessary to draw quantitative conclusions. Thus, we also assess the current status of computational modeling of this kind of impact event, specifically addressing recent work bearing on the sensitivity of such modeling to the equations of state and certain numerical issues.

History and application of hydrocodes in hypervelocity impact

Abstract Hydrocode enhancements have evolved as a result of the desire of researchers to be predictive, generally for some particular application. A review of the development of hydrocodes is given from a historical viewpoint. The paper then ends with a discussion of possible future enhancements in the codes.

Ballistic performance of confined 99.5%-Al203 ceramic tiles

Abstract An experimental investigation has been performed to investigate the ballistic performance of ceramic tiles as a function of the extent of confinement. A secondary objective of the study was to generate experimental data for ceramic modelling validation studies. Two impact velocities were used for the testing, nominally 1.52 and 1.79 km/s. The depth-of-penetration (DOP) into the backup steel cylinder was the measure of penetration performance. 99.5%-pure aluminium oxide tiles, 2.54-cm thick, were used for the study. Confinement was changed by varying the type and thickness of a cover plate. Differential ceramic tile performance, calculated from the DOP measurements and baseline penetration into semi-infinite steel, varied in the range ≈ 1.5-2.8, depending upon the type of confinement and the impact velocity. The data are compared with other data in the literature, and conclusions are made concerning ceramic tile performance as a function of confinement and impact velocity.

On the LD effect for long-rod penetrators

Abstract A common measure of penetration efficiency is given by the depth of penetration P into a semi-infinite target normalized by the original length of the projectile L. It has been known for over 30 years that P L depends upon the aspect ratio L D for projectiles with relatively small aspect ratios, e.g. 1 ⩽ L D ⩽ 10 . This influence of L D on penetration is referred to as the L D effect. Although observed, the L D effect for large aspect ratio rods is not as well documented. Further, published penetration equations have not included the L D effect for high aspect ratio rods. We have compiled a large quantity of experimental data that permits the quantification of the L D effect for projectiles with aspect ratios of 10 ⩽ L/D ⩽ 30. Numerical simulations reproduce the observed experimental behavior; thus, no new physics is required to explain the phenomenon. The numerical simulations allow investigation of the fundamental mechanics leading to a decrease in penetration efficiency with increasing aspect ratio.