55 69 



THE FACTORS DETERMINING DAMAGE 



The question is often asked, upon what feature of the shock wave 

 does the damage to a plate or diaphragm depend? Is it the maximum pressure, 

 the Impulse or the energy? A related question is the law according to which 

 damage varies with size of charge and with distance. 



The results of this and other analyses indicate clearly that no 

 simple and general answers to these questions are to be expected, but that in 

 special cases a few approximate rules can be given. 



1 . Maximum pressure should be the chief factor determining damage to 

 relatively small structures , namely, whenever the time of action of the pres- 

 sure greatly exceeds both the swing time and the diffraction time for the 

 structure, or T^ » T^, T^ » T^. The rapidity with which the pressure is ap- 

 plied, however, will also be of significance. 



For a diaphragm of radius a Inches, this condition should hold at 

 least for shock waves from charges in excess of 50 a^ pounds. This estimate 

 Is based on T^ = ^ /a = (^^300)^1300 and T, < 0,1a x 10"^ from Equation [68], 

 The condition should be satisfied for Modugno gages in the presence of 

 charges of 10 pounds or over. 



If the diffraction time is also much less than the swing time, so 

 that T^» T » T^, non-compresslve theory can be used, as on page 52. If, 

 furthermore, the application of pressure is gradual, the action is essential- 

 ly a static one and the damage corresponds in the static manner to the maxi- 

 mum pressure. On the other hand, if the pressure is applied rapidly, the 

 damage will be increased in proportion to an appropriate dynamic response 

 factor or "load factor." If the application is effectively Instantaneous as 

 in loading by a shock wave, and if the resistance varies linearly with deflec- 

 tion, as is more or less true for a plate or diaphragm In the plastic range, 

 the deflection should be almost twice the static value. 



Since the pressure due either to shock waves or to gas globe oscil- 

 lations, except near the globe, varies roughly as the cube root of the charge 

 and inversely as the distance, the resulting deflection of a plate should 

 vary in the same way, under the conditions assumed, except that at great dis- 

 tances a large correction for the elastic range will be required; for the 

 pressure p required to give a diaphragm of radius a and negligible thickness 

 a small deflection z is proportional to z ; see Equation [8] in TMB Report 

 490 (17)- Thus the maximum deflection will be approximately, bWyr, where b 

 is a constant, and, from Equation [72a], 



T 1 



-1/^--' = ^/-^ ,„, 



where z, is the deflection at the elastic limit. 



