528 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1952 



This example is illustrated in Fig. 3. 



The question of direction of the x and y axes is simply settled by draw- 

 ing a line through either of the acute angles of the parallelogram, crossing 

 the parallelogram at an angle <^i with the longer side. This line will be 

 parallel to the x direction, which is, according to the convention, that 

 of greatest strain. 



So far no mention has been made of strain in the third dimension; 

 that is, a change in thickness of the sheath. In plastic deformation, the 

 volume change is generally negligible. This requires that 



whence 



KKK = 1 

 1 



X. = 



AxAu 



XmI 



Fig. 3 — A square and the parallelogram resulting from stretching to length 

 ratios \x = 2.1 Al in the x-direction and Xj, = 1.045 in the y-direction. 



Table I 



