﻿to Illustrate Elastic Hysteresis, 



525 



§ 9. Effect of Rapid Periodic Changes of Stress combined 

 ivitli Sloxo Variation of Mean Stress. 



If in § 7, we imagine that F changes slowly and periodi- 

 cally whilst the F — x loop is being rapidly described under 

 the influence of a constant F l3 we get an important case in 

 experimental work. In such a case, we may imagine that 

 the variation in F is so slow and the periodic change of 

 superimposed stress (between limits ±F X ) so rapid, that at 

 any instant the material is always in the asymmetric cyclic 

 state. It is interesting to discuss the loop obtained (if any), 

 by plotting the different values of F against the corre- 

 sponding mean values of x for the rapidly described 

 hysteresis loops. We may call such a diagram a mean- 

 stress-strain loop (see Smith & Wedgwood, loc. cit. p. 318). 



There are three cases to consider : — 



(a) If the limits of stress Fq+F^ F — F l5 are such that 

 the corresponding points in the F — x diagram lie between 

 the lines KL and MJ of fig. 4, then the mean-stress-strain 



loop reduces to a straight line. This straight Jine will either 

 be a portion of the line PON, or a portion of some line 

 parallel thereto. For the neutral condition, the points 

 P x and Nj which limit this type of mean-stress-strain curve, 

 will clearly have values of F given by minus and plus 

 respectively an amount given by subtracting the amplitude 

 of Fi from the value of F at N (see fig. 7). 



Qj) Using F | and F-j as amplitudes or positive limiting- 

 values, we may still consider the case of WA less than the 



