P-a model

Fig. 6.4. At relatively low pressures the shock speeds observed for stress waves in low density powder compacts are dominated by the crush-up of the powder toward solid density. The figure shows measured wavespeeds for a range of densities and fits to the data based on Herrmann s P-a model on Fe. Note the unusually low wavespeeds compared to solid density (after Herrmann [69H02]).

Table 6.2 summarizes the low pressure intercept of observed shock-velocity versus particle-velocity relations for a number of powder samples as a function of initial relative density. The characteristic response of an unusually low wavespeed is universally observed, and is in agreement with considerations of Herrmann s P-a model [69H02] for compression of porous solids. Fits to data of porous iron are shown in Fig. 6.4. The first order features of wave-speed are controlled by density, not material. This material-independent, density-dependent behavior is an extremely important feature of highly porous materials. 

For the two explosive loading systems used, the initial pressure wave into the powder is relatively low, varying from perhaps 1.5-4 GPa. In such cases the most relevant compression characteristic of the powder compact is its crush strength , i.e., the pressure required to compress the porous compact to solid density. In the simulations, this strength can be varied over a wide range with the P-a model. The wavespeed of the initial waves was modeled on the basis of shock-compression data on rutile at densities from 44% to 61% of solid density [74T02]. 

Beeause of its emphasis on eonsistent thermodynamies, the csq eode does not permit the use of a P-a model for the erush-up behavior of the powder. Thus, it was neeessary to draw upon the experience in the one-dimensional simulation to select appropriate shock-compression materials behaviors. The... 

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Not unexpectedly the systems that have received the most attention are derivatives of cyclohexane containing a silicon or phosphorus heteroatom. Although cyclohexane is a saturated system, the results of these studies should provide insight for future work on unsaturated systems. Until future studies provide data to the contrary, it will be assumed that Si provides the model for Group IV heteroatom behavior and P a model for Group V behavior. The first aspects to be considered are associated with ground-state geometry and substituent preference. 

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