405 



total energy of explosion E to the initial kinetic energy of the 



2 

 plate gives the following value for o( : 



<'^' — ^^ :^ -> (54) 



where a is the initial thickness of the plate and er- is the yield 

 stress of same. 



Beyond the assumption that it is a constant, the energy 

 fraction ^ will be treated as an empirical constant. If the energy 

 delivery were 100 percent efficient in each element of solid angle 

 cutting the plate, ^ would equal 1/2 since the plate subtends a solid 

 angle of 2 TV out of a raaxirauin of 4Tf. If the energy delivery were 

 50 percent efficient, corresponding roughly to utilization of only the 

 primary shock-wave energy, then ^ would equal 1/4, and so forth. These 

 statements are offered only as a guide in interpreting the empirical 

 values of ^ to be obtained. 



The distribution of strains is given by 



£.-e,- ^^W^'Z-^'Ctc,^), (55) 



with PC given by Jiq. (54), and where C and ^ are the meridional 



and circumferential strains, respectively. The function h*"^/^-' (x, "C") 

 is discussed and tabulated in Sec. 3. The ma:cLniujd central strains are 

 given by 



e,= €.a = €--K = % ^>^ ■ (56) 



The dimensionless constant h^^'^^ is equal to 0.0932. The criterion 



m 



of rupture, the principal thing of interest here, is then given by the 



86 



