COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING \MATERIALS. 187 
detected under the microscope, unaffected by plastic strain.* The effect 
of the increase of temperature which promotes recovery of elasticity must 
therefore be upon the material which, according to Beilby,t exists in an 
altered physical and perhaps molecular condition between the slipped 
surfaces; or, at any rate, upon material in the imniediate neighbourhood 
of these surfaces. 
Recovery, then, is due to the effect of temperature on this material, 
resulting in the healing up of the crystalline ships. It seems reasonable to 
suppose the disappearance of ‘ elastic’ after-strain to be a phase of this 
healing process, rather than a distinct and different phenomenon. The 
fact that recovery is much impeded or totally stopped in the case of iron 
and steel at a temperature of 0° C. shows that rest, unless accompanied by a 
suitable temperature, is ineffective in promoting restoration of elasticity ; 
the rapidity of recovery—i.c., the duration of rest required—being thus a 
function of the temperature. 
Turning now to the consideration of cyclically applied stresses, Ewing 
has remarked: { ‘ When in the overstrained condition, and before re- 
covery has taken place, iron and steel exhibit much hysteresis in the rela- 
tion of extension to load. Any process of loading and unloading, repeated 
until the changes become cyclic, then shows a well-marked difference in 
the length of the piece for any one amount of load in the two stages of the 
process. The curves exhibiting extension in relation to load form a loop, 
and this loop closes up as the piece gradually recovers its elasticity by pro- 
longed rest.’ Recovery of elasticity may thus be defined, for cyclically 
applied stresses, by reference to the hysteresis loop. With regard to the 
physical meaning of this loop, may it be regarded as the cyclic counterpart 
of the elastic after-strain before mentioned, or is it a combined effect of 
permanent set and elastic after-strain ? The answer seems to be, in the 
strict sense, neither; for the cyclical application of stresses, unless very 
slowly made, leaves very little time for the healing during rest. The 
internal condition, then, would appear to be very similar to that of the 
statically overstrained bar immediately after the elastic limit is passed ; 
and when, therefore, no period of rest has differentiated the strain into 
elastic after-strain and permanent set. 
In the ultimate stage of fatigue, the cracks which finally end in rupture 
are doubtless produced by the continual to and fro sliding along crystalline 
cleavage surfaces. This action causes the attrition and removal of ma- 
terial from between these surfaces (Ewing and Humphrey, No. 27). It is 
reasonable to suppose that such to and fro sliding is in operation from the 
time of appearance of a hysteresis loop; and upon this is based the 
commonly accepted explanation of plastic hysteresis. 
The work of L. Bairstow (No. 4) has thrown much light on plastic 
hysteresis. When the cycles consist of unequal + and — stresses, he has 
demonstrated that, before adjustment of elastic limits to a range of stress, 
the hysteresis loop is not closed ; and that plastic hysteresis then consists 
of a cyclical strain, called by him ‘ cyclical permanent set,’ which is accom- 
panied by an average strain of gradually increasing amount, named (the 
tensile maximum stress being greater than the compressive) ‘ permanent 
extension.’ If the range is not too great, the ‘ permanent extension’ 
* Rosenhain, Iron and Steel Inst. Journal, vol. lxx.; 1906. 
+ The hard and soft states in metals, Hngineering, May 19, 1911. 
{ Strength of Materials, Art. 41, 
