Charles L. Mader

THERMAL INITIATION OF EXPLOSIVES

Numerical solutions have been obtained for the nonlinear heat conduction equations arising in the theory of thermal explosions. Explosion times are calculated for externally heated spheres, cylinders, and slabs of several explosive materials, and the results are shown to agree with experiment.

Technique for the Determination of Dynamic‐Tensile‐Strength Characteristics

A technique for the examination of the dynamic‐tensile‐strength characteristics of materials is presented. The dependence of tensile strength upon stress gradient, hence stress rate, is demonstrated for Al, Cu, Ni, and Pb. The results were tested and found to be self‐consistent in that once the dynamic‐tensile‐strength characteristics have been measured they can be incorporated into the numerical calculations, which then can be used to predict complex multilayer spall behavior even in layers of dissimilar materials.

Shock and Hot Spot Initiation of Homogeneous Explosives

The shock initiation of detonation in nitromethane, liquid TNT, and single‐crystal PETN has been studied using a numerical method for solving the reactive fluid‐dynamic equations. Agreement was obtained with previously reported experimental results.Studies were made which explain in detail the mechanism of initiation of detonation at hot spots created by the interaction of a shock with an inhomogeneity. Energy transfer is accomplished by shocks and rarefactions. It is shown how experimentally observed criticality in bubble size can be related to the divergence rate of the shock, and to other features of the fluid flow. The relation of these results to initiation of detonation in inhomogeneous explosives is discussed.

Tsunami Produced by the Impacts of Small Asteroids

ABSTRACT: The fragmentation of a small asteroid in the atmosphere greatly increases its cross section for aerodynamic braking, so ground impact damage (craters, earthquakes, and tsunami) from a stone asteroid is nearly negligible if it is less than 200 meters in diameter. A larger one impacts the ground at nearly its velocity at the top of the atmosphere producing considerable impact damage. The protection offered by Earths atmosphere is insidious in that smaller, more frequent impactors such as Tunguska only produce air blast damage and leave no long‐term scars on the Earths surface, while objects 2.5 times larger than it, which hit every few thousand years, cause coherent destruction over many thousands of kilometers of coast. Smaller impactors give no qualitative warning of the enormous destruction wrought when an asteroid larger than the threshold diameter of 200 meters hits an ocean. A water wave generated by an impactor has a long range because it is two‐dimensional, so its height falls off inversely with distance from the impact. When the wave strikes a continental shelf, its speed decreases and its height increases to produce tsunamis. The average runup in height between a deep‐water wave and its tsunami is more than an order of magnitude. Tsunamis produce most of the damage from asteroids with diameters between 200 meters and 1 km. An impact anywhere in the Atlantic by an asteroid 400 meters in diameter would devastate the coasts on both sides of the ocean by tsunami over 100 meters high. An asteroid 5 km in diameter hitting in mid Atlantic would produce tsunami that would inundate the entire upper East Coast of the United States to the Appalachian Mountains. Studies of ocean sediments may be used to determine when coastal areas have been hit by tsunamis in the past. Tsunami debris has been found to be associated with the Cretaceous‐Tertiary impact and should be detectable for smaller impacts.

Jet initiation and penetration of explosives

The two-dimensional Eulerian hydrodynamic code 2DE with the shock initiation of heterogeneous explosive burn model called Forest Fire, is used to model numerically the interaction of jets of steel, copper, tantalum, aluminum, and water with steel, water, and explosive targets. The calculated and experimental critical condition for propagating detonation may be described by the Held V/sup 2/d expression (jet velocity squared times the jet diameter). In PBX 9502, jets initiate an overdriven detonation smaller than the critical diameter, which either fails or enlarges to greater than the critical diameter while the overdriven detonation decays to the C-J state. In PBX 9404, the jet initiates a detonation that propagates only if it is maintained by the jet for an interval sufficient to establish a stable curved detonation front. The calculated penetration velocities into explosives, initiated by a low-velocity jet, are significantly less than for non-reactive solids of the same density. The detonation products near the jet tip have a pressure higher than that of nonreactive explosives, and thus slow the jet penetration. At high jet velocities, the calculated penetration velocities are similar for reactive and inert targets. 8 references, 17 figures, 1 table.

Three-dimensional modeling of inert metal-loaded explosives

Abstract The reactive three-dimensional hydrodynamic code 3DE has been used to investigate the reactive hydrodynamics of a matrix of tungsten particles in HMX. A propagating detonation proceeding through the matrix of tungsten particles gives calculated detonation velocities and pressures that are much higher than observed. If the heterogeneous shock initiation Forest Fire rate for HMX is used to describe the reactive kinetics, some of the individual detonation wavelets between the tungsten particles fail. The shocked explosive continues to decompose and release energy after shock passage. Equations of state are described for a tungsten and a leadloaded explosive that reproduce the observed performance of these nonideal explosives. The calibrated equations of state use a partial energy release suggested by the three-dimensional model. Evidence is presented that the explosives have a flat top Taylor wave characteristic of weak detonations.

Three-dimensional modeling of shock initiation of heterogeneous explosives

The basic processes in the shock initiation of heterogeneous explosives have been investigated theoretically using a model of a cube of nitromethane containing 91 cubic air holes. The interaction of a shock wave with the density discontinuities, the resulting hot spot formation and interaction, and the buildup to propagating detonation were computed using three-dimensional numerical Eulerian hydrodynamics with Arrhenius chemical reaction and accurate equations of state. The basic process in the desensitization of a heterogeneous explosive by preshocking witha shock pressure too low to cause propagating detonation was numerically modeled.

Three-dimensional modeling of explosive desensitization by preshocking by

Abstract The reactive three-dimensional hydrodynamic Code 3DE has been used to investigate the reactive hydrodynamics of desensitization of heterogeneous explosives by shocks too weak to initiate propagating detonation in the geometries studied. The preshock desensitizes the heterogeneous explosive by closing the voids and making it more homogeneous. A higher pressure second shock has a lower temperature in the multiple shocked explosive than in single shocked explosive. The multiple shock temperature may be low enough to cause a detonation wave to fail to propagate through the preshocked explosive.

Numerical modeling of the effect of temperature and particle size on shock initiation properties of HMX and TATB

Abstract The three-dimensional Eulerian reactive hydrodynamic code 3DE has been used to investigate the effects of particle size (and the remaining void or hole size) and of initial temperature on the shock initiation of heterogeneous explosive charges of HMX and TATB. Shocks interacting with HMX and TATB containing various hole sizes have been modeled. The void fraction was held at 0.5% while the spherical hole sizes were varied from 5.0- to 0.00005 mm radius. The shock pressure was also varied. As the hole size in TATB was varied from 5.0 to 0.5 mm, the explosive became more sensitive to shock. Decreasing the hole size to 0.0005 mm resulted in failure of the shock wave to build toward a propagating detonation. This is similar to the results previously reported for TNT. HMX became more sensitive to shock as the hole size was varied from 0.5 to 0.005 mm. The hole size had to be decreased to 0.0005 mm before the explosive became less shock sensitive. Smaller hole sizes (0.00005 mm) resulted in failure of t...

Detonation induced two-dimensional flows

Abstract Plane wave initiated detonation waves proceeding perpendicular to a confined or unconfined surface exhibit very little wave curvature and a complicated flow pattern behind the wave. Numerical studies of this process have been performed using two-dimensional Lagrangian code, 2DL, to solve the reactive hydrodynamics.