﻿to Illustrate Elastic Hysteresis. 535 



will, of course, correspond to an amount o£ slip given by 

 equation (43). Further increase of F will clearly involve 

 permanent set. 



In the above argument, it is supposed that the variations 

 of F have been made with the range 2 | f\| of the alternating 

 stress kept constant. 



Fig. 12. 



F 



The expression for a typical area of loop in the fgeneral 

 case is complicated, and is not given here. 



For small slips y, it is clear that the results o£ calculation 



for our original model can be used. 



§ 13. Mean-stress-strain Loop for Modified Model. 



Following the argument of § 9, we can consider for the 

 modified model the effects of superposing a periodic slow 

 variation of mean stress on a rapidly alternating stress. 



There are three cases to consider — 



(a) Starting from the neutral condition, provided |F | 

 and IFj) are small enough, the mean-stress-strain curve will 

 be a portion of the straight line PON of fig. 11. The 

 limiting points of this line will be given exactly as in 

 (a) of § 9. 



(6) With | F! | less than F N , but | F | + | F J > F^, we shall 

 get hysteresis loops of the mean-stress-strain type arising. 

 Referring to fig. 13, a typical loop like J 2 K 2 L 2 M 2 will 

 consist of lines J 2 K 2 and L 2 M 2 parallel to the straight line 

 PON, and two curves K 2 NiL 2 and M 2 PiJ 2 . The curve 

 K 2 N!L 2 is clearly obtained as the locus of points G such 

 that GR drawn upwards and parallel to PON from G to R 

 (a point on the curve NL) is exactly equal to |Fi]. The 



