SURFACE AND OTHER EFFECTS 407 



when the excess pressure first reaches zero. If this is true, the time dc 

 Sit which cavitation begins can be obtained by setting P = in Eq. 

 (10.7) with the result 



(10.10) 



-'(j^O 



B. Effect of cavitation on displacement. The occurrence of cavitation 

 in front of a target makes the analysis of part (A) cease to apply after a 

 time ^c, for after this time the water in front of the plate is at a constant 

 pressure very nearly zero. Under these circumstances the plate will be 

 subjected to a very small loading by the pressure behind the plate, and 

 its velocity at this time, which can be calculated from Eq. (10.7), will 

 only very slowly be reduced to zero. 



No structure can in actual fact be considered as infinite without 

 constraint or support. To be more reahstic, the simple model of a free 

 plate must therefore be modified to include the resistance of the struc- 

 ture to deformation and also include diffraction of the incident pressure 

 wave resulting from the finite extent of the targets. These more elab- 

 orate considerations are briefly discussed in the next section. The re- 

 sults so far considered, although of only very Hmited apphcation in 

 practical problems, do illustrate simply the importance of cavitation as 

 a determining factor in underwater explosion damage. The time at 

 which cavitation may be expected to set in is conveniently estimated in 

 many cases by Eq. (10.10), which serves as a convenient although rough 

 criterion in more complex problems than the simple case for which it 

 was derived. 



10.5. Plastic Deformation and Diffraction Effects 



The analysis of the preceding section concerns the simplest possible 

 type of structure or target, the only complication introduced being the 

 inertia of a plate assumed to undergo no deformation by action of ap- 

 plied pressure. Although the analysis of this simple case does illustrate 

 the significant role which cavitation may play in determining explosion 

 damage, it does not bring out other factors which are equally significant 

 in more reahstic cases. The nature and effects of some of the more im- 

 portant of these factors are illustrated in the relatively simple case of a 

 thin circular diaphragm supported at its circumference. The large 

 amount of experimental and theoretical work which has been done on 

 this problem gives a rather clear picture of the important phenomena 

 which may be expected to take place in other problems also, and the 

 circular diaphragm is thus of interest in a general understanding of ex- 

 plosion damage. 



The problems encountered in analyzing the motion of a diaphragm 



