SURFACE AND OTHER EFFECTS J^23 



to this kinetic or afterflow energy of the "kinetic wave" as a factor in 

 damage, particularly close to the charge. This conclusion is surely both 

 misleading and erroneous, if there is implied the existence of effects not 

 determined by the associated pressures (see section 9.2). There is, 

 however, the perfectly valid possibility that, in the region of high pres- 

 sures close to the charge, pressures following the initial peak value of 

 the shock wave are large enough to be effective for much longer times 

 than at greater distances. This fact, and the fact that a greater frac- 

 tion of the radiated shock wave energy is available for mechanical work 

 in near-contact explosions, must be considered in analysis of any data or 

 arguments presumed to establish the importance of afterflow energy, 

 "kinetic waves," or "schubenergie." 



B. Dependence of damage on nature of applied pressure. In idealized 

 examples of a circular plate undergoing plastic deformation, it is found 

 that the damage resulting from pressure waves depends very much on 

 the relative dimensions and characteristic times of the plate and the 

 pressure wave. Similar differences must be expected for other struc- 

 tures, and the property or properties of the pressure wave which are of 

 importance more generally can be qualitatively inferred from these re- 

 sults. Characteristic times which must be significant are: the duration 

 of the incident pressure (e.g., time constant of an exponentially decaying 

 wave), the natural response times or frequencies of the structure (e.g., 

 the plastic time of a circular plate) , and the diffraction times, determined 

 by dimensions of the structure, required for equalizing diffracted pres- 

 sure waves to be propagated over the structure. 



If the duration of the pressure wave is much shorter than other 

 times, the effect of pressure is essentially that of a local impulsive blow 

 on all parts of the structure, which then moves in a manner determined 

 by the impulse of the wave. This impulse varies for a given explosive 

 roughly as W^'-^/R, where W is the charge weight and R the distance. 

 This state of affairs can be realized only for relatively large structures 

 with slow response, and will not be realized unless the structure is suffi- 

 ciently rigid to prevent cavitation in the time interval before rarefaction 

 pressures can be equalized by diffraction waves. Some criterion as to 

 occurrence of cavitation must therefore be applied to determine whether 

 analysis based on superposition of pressures, which asymptotically in- 

 volves the impulse of the wave, can be applied. 



In the extreme that the duration of the wave is much longer than the 

 response time or diffraction time, the wave will act much more like an 

 applied static pressure. In the case of a shock wave, the initial peak 

 pressure will come to be the controlling factor, as will the peak value of 

 bubble pulse pressure (although its rate of rise may also be significant). 

 The peak shock wave pressure varies with charge weight and distance 

 roughly as |fo-38/^i.i4 f^^. j-^nges of interest, whereas slightly smaller 



