Experiment propagation

Before the critical distances for the propagation of explosions in sand are measured, one must find one of the most sensitive explosives in use today. If one knows the distance needed between two samples of this most sensitive explosive to insure that no propagation takes place, other less sensitive explosives will not experience propagation of explosions if separated by this critical distance. 

The crystalline phase affects the viscoelastic dynamic functions describing the glass-rubber relaxation. For example, the location of this absorption in the relaxation spectrum is displaced with respect to that of the amorphous polymer and greatly broadened. Consequently, the perturbing effects of crystal entities in dynamic experiments propagate throughout the amorphous fraction. The empirical Boyer-Beaman law (32)... 

In the present experiments, propagating interactions were observed to occur consistently in a stratified molten-tin water system confihed within a narrow channel for water depths above a threshold value. The existence of a critical water depth required to support a propagating Interaction may explain the irreproducible behavior observed by Anderson et al. Herein,... 

First order stimulated Stokes scattering experiences an exponential gain in intensity as the fields propagate tlirough the scattering medium. This is given by the expression [75]... 

In experiments, the two symplectic methods ROT and SPL performed very similarly in terms of error propagation and long term stability. The ex-... 

The models you use to portray failures that lead to accidents, and the models you use to propagate their effects, are attempts to approximate reality. Models of accident sequences (although mathematically rigorous) cannot be demonstrated to be exact because you can never precisely identify all of the factors that contribute to an accident of interest. Likewise, most consequence models are at best correlations derived from limited experimental evidence. Even if the models are validated through field experiments for some specific situations, you can never validate them for all possibilities, and the question of model appropriateness will always exist. 

Shock-compression processes are encountered when material bodies are subjected to rapid impulsive loading, whose time of load application is short compared to the time for the body to respond inertially. The inertial responses are stress pulses propagating through the body to communicate the presence of loads to interior points. In our everyday experience, such loadings are the result of impact or explosion. To the untrained observer, such events evoke an image of utter chaos and confusion. Nevertheless, what is experienced by the human senses are the rigid-body effects the time and pressure resolution are not sufficient to sense the wave phenomena. 

When an isotropic material is subjected to planar shock compression, it experiences a relatively large compressive strain in the direction of the shock propagation, but zero strain in the two lateral directions. Any real planar shock has a limited lateral extent, of course. Nevertheless, the finite lateral dimensions can affect the uniaxial strain nature of a planar shock only after the edge effects have had time to propagate from a lateral boundary to the point in question. Edge effects travel at the speed of sound in the compressed material. Measurements taken before the arrival of edge effects are the same as if the lateral dimensions were infinite, and such early measurements are crucial to shock-compression science. It is the independence of lateral dimensions which so greatly simplifies the translation of planar shock-wave experimental data into fundamental material property information. 

Conservation relations are used to derive mechanical stress-volume states from observed wave profiles. Once these states have been characterized through experiment or theory they may, in turn, predict wave profiles for the material in question. For the case of a well-defined shock front propagating at constant speed L/ to a constant pressure P and particle velocity level u, into a medium at rest at atmospheric pressure, with initial density, p, the conservation of momentum, mass, and energy leads to the following relations ... 

The pressure is to be identified as the component of stress in the direction of wave propagation if the stress tensor is anisotropic (nonhydrostatic). Through application of Eqs. (2.1) for various experiments, high pressure stress-volume states are directly determined, and, with assumptions on thermal properties and temperature, equations of state can be determined from data analysis. As shown in Fig. 2.3, determination of individual stress-volume states for shock-compressed solids results in a set of single end state points characterized by a line connecting the shock state to the unshocked state. Thus, the observed stress-volume points, the Hugoniot, determined do not represent a stress-volume path for a continuous loading. 

Fig. 2.3. Experimental determination of shock-stress versus volume compression from propagating shock waves is accomplished by a series of experiments carried out at different loading pressures. In the figure, the solid lines connect individual pressure-volume points with the initial condition. These solid straight lines are Rayleigh lines. The dashed line indicates an extrapolation into an uninvestigated low pressure region. Such extrapolation is typical of much of the strong shock data.

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