Sn le a a alin 
COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 18!) 
ture effect on unstable material between slipping cleavage surfaces, it is 
impossible, so far as the writer is aware, to say. 
A point worthy of notice in Bairstow’s experiments (No. 4) is that the 
increase of width of hysteresis loop for a given increase of range applied was 
greatest for equal + stresses. It would be expected that, with the accom- 
panying increase of “ permanent extension * under unequal + stresses, the 
increase of width of loop would have been the greater. That itis otherwise 
indicates that recovery must be in comparatively rapid operation during 
the increase of ‘ permanent extension,’ so as to effect a continuous (because 
less interrupted) healing of the average amount of strain per cycle. 
In view of Coker’s (No. 18) and McCaustland’s (No. 55) conclusions 
concerning absence of recovery at 0° C., experiments such as Bairstow’s, 
conducted at 0° C., should throw light on the operation of recovery, 
especially in the case of cycles of unequal + stresses. Hopkinson has 
already suggested that his own experiments (No. 43) should be carried 
out at higher temperatures. 
Elastic Hysteresis. 
When a metal is put through a cycle of stress of which the extreme 
stresses are less than any known elastic limit or limits of the material, the 
stress-strain diagram is found to be not a straight line, but a closed curve 
containing a very small area (No. 26). The name of ‘ elastic hysteresis ’ is 
given to this phenomenon ; its physical nature is not understood.* A 
review of recent papers on the subject is given in Appendix I. of this 
Report. 
its the first place, there is ground for belief that the increased decrement 
which has been observed after long-continued torsional oscillation of wires, 
and the subsequent decrease of decrement with rest, are accidental circum- 
stances pertaining to the use of wires in decrement experiments, but other- 
wise quite extraneous to the phenomenon of elastic hysteresis. The draw- 
Ing process of wire-manufacture renders material liable to give abnormal 
results, and it appears probable that these effects are due to crystalline 
cleavage slipping, of which they are quite characteristic. Hopkinson and 
Williams (No. 45) found no perceptible increase of hysteresis with a quarter 
of a million stress-cycles on a steel bar; correspondingly, if no ‘ fatigue of 
elasticity ’ (as this alleged increase of hysteresis has been called) occurs 
there would be no corresponding recovery of elasticity. Should this 
absence of fatigue of elasticity be supported by further experiment, 
alleged points of resemblance between elastic hysteresis, and fatigue of 
strength and recovery of elasticity in plastic hysteresis, would disappear. 
It may be remarked that there is good ground for believing that elastic 
hysteresis will always accompany plastic hysteresis. The latter is an 
aggregate effect of movements in the crystals, and is of much greater 
- magnitude than the former ; butit seems clear that in general the cleavage 
slipping of plastic hysteresis affects at the same time only parts of a por- 
tion of the whole number of crystalline grains composing a material ; thus 
the remaining parts and grains will doubtless be affected with elastic 
hysteresis. 
The chief contrast between the two kinds of hysteresis is furnished by 
* The following articles should be consulted : ‘ Viscosity of Solids,’ Art. 54; 
Love's Theory of Elasticity; Art. 56, Ewing’s Strength of Materials; Article ‘ Elasti- 
city,’ Lord Kelvin, Ency. Brit., 9th ed., vol. vii, 
