530 



Figure 8 shows the comparison between a theoretical damage versus 

 weight curve based on theoretical shock-wave parameters and the experi- 

 mental damage results. Considering the fact that the only experimenteil 

 values used in determining the theoretical curve were the dimensions of 

 the gauge and the yield stress of the diaphragms, the agreement (ca. 15^) 

 is excellent. 



2. Copper Diaphragms 



It is difficiilt to apply Kirkwood's damage equations to copper 

 diaphragms because copper does not have a definite yield stress like 

 that of steel nor was the theory intended to apply to copper. Figure 9 

 shows that a theoretical curve based on a yield stress of 5,000 lbs/in. ^ 

 passes through the empirical damage-weight curve, but has a markedly 

 greater slope. The slope of the theoreticeil curve is gradually decreased 

 by assuming greater yield stress, but such a procedure rapidly changes 

 the absolute level of the curve, as is illustrated by the example in 

 which the yield stress was taken as 20,000 lbs/in. It is evident that 

 the low weight exponent (i.e., slope of the damage-weight curve plotted 

 on log-log paper) found for copper diaphragms is difficult to reconcile 

 with the Kirkwood damage equations. It is possible that work hardening 

 is a relatively important factor in the damage process for copper. 



V. RESULTS OF EXPERIMENTS 



1. The Bnpirical Equation of Damage 



The "damage" recorded by a deformed diaphragm can be measured in 

 terms of two simple parameters of the deformation, namely, the volimie 

 of the "dish", or the maximum depth of this dish. Since the latter 

 measurement was easier to make acciirately, and since it seemed to be 

 reproducible, only this measurement was made for most work, and it was 

 arbitrgirily defined as damage. 



It had previously been foundi/ '_/ that the maximum depth of 

 depression of a deformed diaphragm could be expressed fairly accurately 

 over a considerable range of experimental conditions by the following 

 empirical equation: 



D = k !! (7) 



d" 



where D is the maximum depth of depression, or damage, 



k is a constant determined by the properties of the explosive, the 

 ~ properties of the diaphragms, and by the units used for the other 

 quantities, 



W is the weight of the explosive charge. 



12/ Cf . for instance, reports from the Mine Design Department of the 

 British Admiralty 



