Thus, the resulting equation for prediction of instability-type failure 

 in acrylic plastic shells can be stated as 



m^a(f 



^ 



(4) 



*V 



When this formula is utilized, it is imperative that in order for the formula to 

 predict critical pressure of an acrylic plastic sphere the material properties 

 used in the formula must be obtained under stress rates that are identical to 

 that used for implosion of the sphere. In practice, this means that, when the 

 Equation 4 is used to predict the critical pressure of an acrylic plastic sphere 

 under a short-term pressure loading condition (pressurization at some constant 

 rate to implosion), the stressing rate of the material test specimens should be 

 the same, or very close to the stressing rate of the sphere. 



Thus as the first step in calculating the thickness of the spherical 

 capsule, a stress— strain relationship had to be established for grade G 

 Plexiglas under a stressing rate similar to the one to be used in short-term 

 implosion tests of acrylic plastic capsules. Since the stress rate tentatively 

 selected for capsule implosion tests was to be in the 800-to-1,000-psi/min 

 range, similar stressing rates were used to determine the material properties 

 of acrylic plastic (Figures 14a through 14d). 



Utilizing the E s , E t , and /x v determined by uniaxial tests and 

 simultaneously solving Equations 3 and 4, the wall thickness required for 

 implosion by the mechanism of general elastoplastic instability failure was 

 calculated to be t/R = 0.0685 and the average membrane stress at critical 

 pressure s avg = 10,200 psi. At a critical pressure of 1,350 psi (equivalent to 

 3,000-foot depth) and an average stress level of 10,200 psi, the mechanical 

 properties of acrylic plastic were determined to be E s = 402,000 psi, E t = 

 270,000 psi and m v = 0.375 (Figures 14a through 14d). 



Once the t/R proportion of the sphere was established at 0.0685, 

 detailed calculation of stresses could take place. Using the analytical expres- 

 sions for distribution of stresses in a thick-walled sphere of elastic material 



S 1 = S; 



R 3 (R: 3 + 2r 3 ) 



2r 3 (R f 



Ri 3 ) 



(5) 



S, = 



R Q 3 (r 3 - R, 3 ) 

 r 3 (R 3 - R^) 



(6) 



32 



