555 



h. Experiments Designed to Test Predictions of Diaphragm Deformation 

 Theory . 



(a) Effect of variation in diaphragm thickness on deformation . 

 When Lot 3 steel diaphra_^s '<ere first received, it was foiind that the 

 thickness of these diapliragms varied from .075 to .09'»- in. In Lot 1 ajid 

 Lot 2 diaphragms the variance had not been greater than .002 in. If 

 Lot 3 diaphragms were to be used, it was necessary to establish a method 

 of correcting the damage obtained with a diaphragm of a given thickness 

 so that it would be comparable with that of a diaphragm of another 

 thickness. 



(i) Derived from theory . Consider Equation (l) and Equation (2) 

 of Section III. Substituting typical values for the constaints (Ti> , /* , 

 //**„ , and ao in Equation (2), namely 60,000, 7.8, 1.01, and O.O85, 

 respectively, the value 661O sec"-'- is obtained for CJ . If a^ is not 

 0.085 but 0.075, U) becomes 63i^O sec"^, a change of k.li,. For nonc^ of 

 the small scale work discussed in this report was the time-constant (9) 

 of the shock wave at the gauge positions greater than 0.25 x 10~3 sec 

 (the time-constant of a shock wave 8 ft. from a 25 lb. TNT chargeiZ') 

 so an upper limit for the value of CO © woiold be about 1,65. Then a 

 diaphra-gm thickness variation from .085 in. to .075 in. or to .095 in. 

 would change the corresponding value of g by 2% at the most (much less 

 for a single shot), see Table II. 



Let us now assume that g is independent of a over the range of 

 variation of a encountered, and consider the ratio of damages predicted 

 by Equation (l; for two diaphragms of different thicknesses, other con- 

 ditions be^ng held constant. It is easily deduced that the ratio of 

 damage {Z^ ) of a diaphragm of a given thickness {slq') to the damage (Zj^) 

 of a diaphragm of standard thickness (ag) is 





^o 



.1J^5 



^o VV+^1^ 



1/2 



1 

 " X 



(26) 



If the diaphragm thickness is varied from a standard value of .085 in. 

 to .075 in., the damage is increased $%. 



It appears, than, that the contribution of the g term variation to 

 the variation in Z^ caused by different diaphragm thicknesses is of 

 second order, in no case more than about l8^ of the total damage variation 

 due to different thicknesses for the experimental conditions employed. 

 This enables the calculation from Equation (26) of a reasonably accurate 

 set of correction factors, independent of the yield stress of the steel 

 and of the peak pressure and time-constant of the particular shock wave 



15/ WDRC Division 8 Interim Report Underwater Explosives and Explosions, 

 UE-16, p. 10, December 19^3. 



