strength at the expense of higher stresses (see Figure 7), would give rise 

 to higher overall collapse strength. Based on the theoretical stresses 

 given in Figure 7 and using a yield strength of 120, 000 psi, yielding ac- 

 cording to the Hencky-Von Mises criterion would initiate at the most highly 

 stressed region of Model OV-5 at a pressure of 7240 psi as compared with 

 a pressure of 7500 for the configuration of Model OV-4. 



Both models failed by inelastic general instability.. Although no rig- 

 orous method presently exists for computing the elastic general-instability 

 strength of sandwich cylinders, an extension of the well-known criteria 

 and formulas used for conventional ring -stiffened cylinders permits an 

 order-of-magnitude determination for the present cases. The well-known 

 and convenient Bryant formula^ was used for this purpose. Calculation of 

 the "shell-term" was based on the assumption that the two sandwich shell 

 elements constituted the membrane contribution to the buckling strength; 

 the combined shell thickness was assumed to be at a radius equidistant be- 

 tween the radii of the two concentric cylinders. The bending contribution 

 to the buckling strength, that is, the "frame -term" in Bryant's formula, 

 was computed for a "free" ring having the actual sandwich cross section 

 shown in Figure 2 for each case. 



Table 2 lists the elastic general-instability pressures computed by 

 the above procedure, using elastic modiili of 16 x 10° psi for titanium and 

 30 X 10 psi for steel. It is seen that the elastic general-instability pres- 

 sure for the four-diameter -long model of the original design (OV-4) is 

 only one -half that for both the one -diameter -long model (OV-3) and the 

 four-diameter-long model of the suggested redesign (OV-5). 



The elastic general-instability pressures listed in Table 2 are based 

 on the assumption that the stresses in the sand'wich structure are within 

 the proportional limit of the material. However, this was not the case 

 for the models tested. For Models OV-4 and OV-5, the elastic -instability 

 pressures were effectively reduced as a consequence of the curvilinear 

 nature of the stress-strain curve (see Figure 20) for the titanium material 

 to such a state that inelastic general instability, or buckling at a reduced 

 modulus, became the determinative factor of collapse. 



To determine the inelastic general-instability collapse pressure p 

 for cases where the stresses exceed the proportional limit, the following 



29 



