﻿512 Mr. S. Lees on a Simple Model 



Messrs. Smith & Wedgwood, 'Journal of Iron and Steel 

 Institute,' vol. xci. p. 374. It must be admitted that in one 

 important respect, the results of these authors appear to 

 differ from those of other experimenters ; in that, according 

 to the cited authors, elastic hysteresis would appear only to 

 make itself evident under certain conditions, whereas other 

 experimenters have been of opinion that elastic hysteresis * 

 always occurs with stress change, even with small range of 

 stress. Without expressing any opinion on the existence or 

 not of elastic hysteresis with small ranges of stress, the 

 author has taken the results of Smith & Wedgwood, and 

 attempted to construct a simple model illustrating these 

 results. Whilst it is not contended that the model to be 

 described is the best possible, it does to some extent satisfy 

 a desire to reduce to simple mathematical treatment many 

 of the well-known elastic phenomena. 



It may be here noted that the model described below 

 in § 3, and the modification of § 9, between them illustrate a 

 whole series of well-known phenomena, such as : 



(i.) Existence of elastic hysteresis loops only under certain 



conditions, 

 (ii.) Small variation of area of loop with speed of 



description, 

 (iii.) General shape of loop, 

 (iv.) General character of mean-stress-strain loops obtained 



when slow speed periodic stress is combined with 



rapidly alternating stress, 

 (v.) Existence of two points in loop at which (limits of 



Hooke's law) the loop commences to depart from 



the straight line law. 

 (vi.) The production of permanent set in a material and 



the existence of a true elastic limit beyond which 



elastic recovery is infpossible. 

 (vii.) The existence of a yield point, 

 (viii.) The general relationship between elastic hysteresis 



and the three conditions referred to in (v.), (vi.), 



and (vii.). 

 (ix.) The phenomena of slip bands, 

 (x.) The effect of overstrain on the two points of (v.). 



So far as the author knows, such a model with its illustra- 

 tions as above, is original. 



Before describing the model, some reasons for ruling out 

 ordinary viscous fluid effects as the predominating cause of 

 elastic hysteresis will be given. 



* Diminishing, of course, with the range of stress. 



