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The standard way of parametrizing a steady structured shock is by plotting the stress jump across the wave (Δσ) versus its maximum strain rate (ε) on a logarithmic plot. Doing so one usually gets a straight line, which means that ε ∝ (Δσ)β . Grady and coworkers noticed in the 1980s that for many materials β=4. Since then several workers in the field tried to understand this unusual behavior, but no satisfactory explanation was found. Recently Grady revisited the fourth power law with an extensive review, including descriptions of the various mechanisms proposed as possible explanations. In view of this background we use here the fourth power law to calibrate the strain rate component of the constitutive response of Al 6061-T6. To this end we integrate the steady viscoplastic equations (developed long ago) from the elastic precursor level to the stress plateau level. We find that the plastic deformation rate has to depend on the deviator overstress by dp ∝ (s -- ⅔Y)α with α=2.38. But for high shock levels, when the elastic precursor is overdriven, using this value of a leads to a higher value of the slope β, close to β=6. [ABSTRACT FROM AUTHOR]

According to detonation shock dynamics (DSD), the normal front velocity at any point on a detonation front is Dn(k), where k is the local mean curvature. In rectangular coordinates a point on the front therefore moves according to: dx/dt=Dncos(n,x), dy/dt=Dncos(n,y) and dz/dt=Dncos(n,z). The direct DSD algorithm makes use of these simple equations. We define the detonation surface by putting discrete points on it as densely as needed. At each point we have the above three ODEs. For n such points we therefore have a system of 3n ODEs. We propagate the front by solving them simultaneously, where we calculate the mean curvature k by a finite difference approximation. At the boundaries we apply the limiting angle constraint. In the paper we demonstrate the use of the direct algorithm for a special relatively easy case of detonation in a bar with a rectangular cross section, with different values of a/b. We compute the size effect curves and compare with the diameter effect curve of a circular bar of the same cross section area. [ABSTRACT FROM AUTHOR]

When a long rod projectile hits a ceramic target, the projectile may sometimes dwell at the target boundary and flow radially. This dwell or interface defeat phenomenon has to do with the dynamic failure process of the ceramic target material. As ceramics are brittle materials, what is needed to model dwell, is a realistic model for dynamic failure of brittle materials. A "standard" such model is the so called JH model (which has several versions). According to JH the material accumulates damage as a function of the effective plastic strain, which is a ductile response feature. Brittle materials are not supposed to accumulate plastic strain before they're fully failed. To model dwell we therefore propose here a different failure model. We call it BSF (= Brittle Shear Failure), and it is based on the Overstress (or overload) principle. Our BSF model is rather simple, has a small number of adjustable parameters, and is readily calibrated. We implement the model in a hydro-code and demonstrate how it works for a typical example of dwell situation. In the example, a long steel rod impacts an AD995 alumina target with and without a copper buffer. [ABSTRACT FROM AUTHOR]

DSD makes it possible to calculate propagation of expanding detonation shocks without a need to evaluate the flow field behind them. DSD is a quasi steady state model calibrated from detonation breakout curves of steady detonations, usually in sticks. Once calibrated (normal detonation velocity Dn as function of local curvature k), it is applied to non steady expanding detonation shocks with slowly varying shapes. Time dependent Dn(k) relations were introduced in the past in forms like Dn(k,dk/dt) or k(D, dD/dt), but we’re not aware that such relations were calibrated or applied to realistic detonation situations. In this context its worth mentioning, that many detonation configurations do not evolve towards steady state. In this paper we check predictions of DSD in a spherical outgoing detonation, which is non-steady, by comparing them to reactive flow calculations. From the results we conclude that: 1) for each initial state (in D(R) plane, say) we get a different shock path. All shock paths converge for large R; 2) detonation acceleration dD/dt depends on detonation velocity through: dD/dt = A(DCJ-D), where A depends on the initial radius; 3) the various detonation shock paths do not coincide with the Dn(k) relation obtained by solving the eigen value problem of quasi steady detonation in spherical symmetry. [ABSTRACT FROM AUTHOR]

Understanding the mechanics of interaction of a long rod projectile with a forward moving plate at an angle is essential to understanding long rod interaction with an explosive reactive armor cassette. To investigate the mechanics of such an interaction we use AUTODIN2D/EULER in plane geometry, although the problem is 3D. We assume that this is a satisfactory approximation, as we're only interested in the main features, and are not comparing fine details to experimental results. From the simulations we learn that the interaction never reaches steady state. Initially each material splits into two streams, and the interaction plane is perpendicular to the rod. But with time the interaction plane rotates slowly, until it becomes parallel to the rod, which is then able to continue moving forward without interruption. During this process interacting rod material of length ΔL is diverted at an angle and becomes ineffective for penetrating the main target. We made many such runs to determine the dependence of ΔL on the parameters of the problem. This dependence makes it possible to predict ΔL for a variety of rod-plate situations. [ABSTRACT FROM AUTHOR]

Unlike in metals, stress and particle velocity histories of shock waves in ceramic materials show a typical "ramping" above the Hugoniot Elastic Limit (HEL). Under the assumption that the HEL signifies the beginning of failure of the material, this "ramping" has been described by viscoplasticity or by moduli degradation. However, there is ample experimental evidence to rule out plastic flow at the HEL level of stress, and it seems improbable that the moduli would degrade significantly during the compressive phase of a plate-impact. The proposed micro-mechanical mechanism for the HEL, and for the ramping beyond the HEL, is based on the process of porous compaction due to pressure above a threshold pressure P[sub crush]. Although the pore volume of high-grade ceramics is quite small, it is sufficient to cause the ramping observed in Hugoniot measurements from the seventies. Additional evidence for the effect of porosity on the HEL stress has been given in recent years. The experimental evidence is supported by simulations, in which a simple model for porous compaction was used. These simulations suggest that porous compaction is the main micro-mechanical mechanism causing the "ramping" and other features related to the HEL. [ABSTRACT FROM AUTHOR]