148 



I 23456789 10 



To, Distonce from Center of Undistorted Diaphragm In inches 



Figure U - Integrated Radial Strain Corresponding to a Station 

 on the Undistorted Diaphragm 



The slope of this curve is the radial strain t.. 



and €., the conventional thickness strain, is 



^0 



"■0 



Since the density of the material remains constant, the convention- 

 al tangential strain e^ can be found from the equation expressing that fact 



(1 + €,)(1 + €,)(1 + e^) = 1 [11] 



or 



tfl = 



1 + €. 



- 1 



:i2] 



The values of these strains were found from the experimental data 

 as follows. A graph was drawn with (s - r^) as ordinate and r^ as abscissa 

 as shown In Figure U. The radial strain «, is obtained by measuring the 

 slope of the curve graphically. 



Since the volume remains constant, 



/Iq X 1 X 1 = /l X I- X Ij 



where Z, and Ij are the final lengths of the sides of the grid and /i^ and h 

 are the original and final thicknesses of the material within the grid. 

 Then 



h '• '^ 



Thus hf^/h is calculated directly from the grid data given in Figure 

 2. €g can then be calculated with the use of Equation [12]. 



In Figure 5 fr s^cl e^ are plotted as ordlnates and r^ is plotted as 

 abscissa. It is interesting to note that the tangential strain €^ Is very 



