Principal Hugoniot

For interactions in which material at a given point experiences only one shock wave and no other shocks or rarefactions, the principal Hugoniot is all that is required to determine the states achieved. In situations in which a material experiences several shocks or rarefactions, using the principal Hugoniot to approximate subsequently shocked or released states may or may not be a good approximation. In this section, only singly-shocked materials at small strains are considered. 

The study of shock-wave equations of state of porous materials provides a means to expand knowledge of the equation of state of condensed materials to higher temperatures at a given volume than can be achieved along the principal Hugoniot. Materials may be prepared in porous form via pressing... 

Figure 4.18. Sketch of Hugoniots of material with different porosities. Isentrope for material is indicated by curve S, along OA. Principal Hugoniot, H, indicated by curve OB. Porous Hugoniots are indicated with initial volumes. shown at O, O", and O " and curves OC, OC", and OC". Normal Hugoniots are indicated for K > k where = (2/ o + 1) 2nd k = Foo/K whereas anomalous Hugoniots are shown for K < k.

Show that, for small strains, the difference between the principal and the second Hugoniot of a material is negligible. 

A limited number of minus-x orientation samples were impact loaded in the vicinity of the Hugoniot elastic limit at stresses from 5.9 to 6.7 GPa. The principal observation of these experiments was that positive currents were observed from negative polarity disks when a stress of 5.9 GPa was exceeded. Such an observation confirms that quartz responds as predicted by the model, and that the elastic limit is in the vicinity of 6 GPa. 

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