Selection of Capsule Dimensions. The acrylic plastic wall thickness 

 was selected on the basis of ( 1 ) elastic theory for stress distribution and 

 (2) elastic instability theory applied to a thick-walled perfect sphere with- 

 out penetrations. These theories provide only approximations. Acrylic 

 plastic is viscoelastic, rather than elastic and thus basically nonisotropic 

 when stressed; the deformation of the material is not simply a function of 

 stress but also of time and modulus of elasticity, which changes from point 

 to point in the acrylic plastic hull according to the stress distribution. 



However, under short-term loading the theory for thick-wall elastic 

 stress distribution gives a good first-order approximation of what the wall 

 thickness of the capsule should be in order to be within a specified com- 

 pressive stress range. Although this theory does not predict the magnitude 

 of stress raisers around the hatches, it was felt that if the average membrane 

 stress level selected is low enough, the increase in stress generated by the 

 presence of steel hatches will not surpass the ultimate tensile and compres- 

 sive strength of the acrylic plastic and will not cause ultimate failure of the 

 acrylic plastic material, although some viscoplastic deformation may take 

 place. 



The elastic stability calculations are also only approximations. The 

 viscoelastic and viscoplastic time-dependent behavior of the acrylic plastic 

 material negates the basic premises underlying the elastic stability calcula- 

 tions. But as in the calculation of stresses, it was felt that a first-order 

 approximation is acceptable so long as the calculation of implosion pressure 

 was limited to (1) the short-term loading case, in which the effect of time 

 on viscoelastic behavior of material is minimized, and (2) the selected 

 implosion pressure was higher than the operational pressure by some 

 reasonably high safety factor. 



Since elastic instability of external pressure hulls for shallow depths 

 is generally the deciding factor in determining wall thickness, 16, 17, 18 it was 

 used as the primary design consideration. The classical analytical expression 

 for elastic instability developed by Zoelly in 1915 was originally derived 16 

 for perfect spheres. 



:e, r: 



^ 



d) 



where p cr = critical pressure at which elastic instability occurs (psi) 

 E = Young's modulus (psi) 

 t = shell thickness (in.) 



30 



