149 



123456789 10 



r^ , Distonce from Center of Undistorted Dioptirogm in incties 



Figure 5 - Observed Radial and Tahgentlal Strain on a 

 Circular Diaphragm under Hydrostatic Pressure 



small at the clamped boundary of the diaphragm. It should be zero if the 

 boundary is perfectly clamped. 



The natural strains are now computed from Equation [1] as (. ^ = 

 In (1 + €^) and (.^ = In (1 + (. ^) . The octahedral shearing strain is finally 

 obtained from the relation 



I VT »/77"T7777TT7 



[6] 



A tabulation of r,,, ( s - r^ ) , e^ , 6^, , /i^A and y is given Ih Table 

 1. The values of t, and e^, were taken from the faired curve of Figure 5- 



A specimen cut from the same plate as the diaphragm was subjected 

 to a standard tensile test. A true stress-strain curve was obtained for this 

 coupon. The r- y curve of Figure 6 is based on this true stress-strain curve. 

 Figure 7 Is the integrated curve with 4\rdy plotted as the ordinate and y 

 as the abscissa. The ordinate gives the energy absorbed per unit volume cor- 

 responding to a given value of y. 



The area of the diaphragm before distortion is divided into eleven 

 annular regions bounded by concentric circles whose diameters are inch, 1 

 inch, 3 inches, and so on. The values of r^ at the points midway between two 



consecutive circles are l/U Inch, 1 inch, 2 Inches, It is assumed that 



the values of y at the stations r^ = 1/4 inch, 1 inch, 2 Inches, .... are the 

 average for the corresponding annular rings. 



