146 



By combining Equations [2], [3], [4], [5], and [8], it has been 

 shown by a number of writers (5) that AE may be expressed entirely in terms 

 of T and y as follows: 



3 



AE=\\Tdy [9] 



2 



If a T-y curve is available from any source, as for example from 

 a simple tensile test, the curve relating AE and y can be obtained by me- 

 chanical integration. It is then relatively easy to calculate the energy 

 absorbed during the deformation of a structure fabricated from the same ma- 

 terial provided the distribution of the principal strains is known. The dis- 

 tribution of the octahedral shearing strains can then be obtained by using 

 Equation [5]. 



The method will be illustrated in detail for the case of a circular 

 diaphragm of medium steel clamped rigidly along its rim and deformed by hy- 

 drostatic pressure. A r-y curve is obtained from a tensile test coupon, and 

 a AE-y curve is obtained by mechanical integration. The distribution of the 

 octahedral shearing strains in the deformed diaphragm is represented by the 

 function y{r^), where r^ is the distance of a particle from the center of the 

 diaphragm before distortion. The corresponding value of AE Is then obtained 

 from the AE-y curve. The total energy absorbed by the diaphragm is given by 



E 



^AE X h^ .X 2TTr^drQ [10] 



where a is the radius and h^ the original thickness of the undeformed 

 diaphragm. 



This method will now be applied to an actual case. 



A medium-steel circular diaphragm was deformed hydrostatically by 

 applying pressures in increments up to T125 pounds per square inch. The dia- 

 phragm had a radius of 10 inches and a thickness of 0.125 inch. The profile 

 of the deformed diaphragm was measured at each successive pressure. The en- 

 ergy required to produce the deformation corresponding to the maximum pres- 

 sure was obtained by evaluating 



I p dv 



This energy was found to be 385,000 inch-pounds. 



A 1 -inch grid was drawn on the diaphragm in its original condition. 

 The final grid measurements are as represented In Figure 2, 



