COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 365 
If the action occurred in.a metal endowed with zero thermal conductivity, we 
might expect that the action would be ideally reversible, the heat given out during 
one stage of the dual change remaining ready to be absorbed in the second stage of 
the action. But in actual metals, of good conductivity, the heat produced in the one 
stage is dissipated by conduction, and in the second stage must be received back 
from the surrounding metal by conduction in the opposite direction. The action as 
a whole must be similar to that.of a reversed heat-engine (refrigerator) taking in a 
quantity of heat at one temperature and giving out a greater quantity at a somewhat 
higher temperature, the balance being made good by mechanical work supplied 
by an external source. A still closer analogy would be that of a refrigerating 
engine working under conditions such that thermal leakage was an important effect. 
The operation of such an engine, thermodynamically irreversible, might still be 
mechanically reversible ; thus the action does not necessarily involve fatigue. 
Hysteretic heating is not, therefore, to be regarded as evidence that the metal will 
necessarily fail from fatigue if the test be continued long enough; but merely as 
evidence of an action that may result in fatigue if the quantities of energy involved 
‘exceed certain limits. The evolution of a given quantity of heat from a large number 
of small zones, each containing only a few molecules, may cause no perceptible growth 
of cavities; but the same evolution of heat from a smaller number of large zones 
may involve so many adjacent molecules in simultaneous movement that orderly 
replacement is impossible, so that change of submicrostructure proceeds apace, 
forming internal cavities that eventually develop into cracks. 
Experimental Evidence of Hysteresis. 
The term ‘ mechanical hysteresis’ has long been used to describe a group of 
actions that occur in metals subjected to cyclic variations of stress, within determined 
limits less than the yield-point. These actions are revealed by phenomena of two 
kinds, viz. (1) the absorption of a quantity of work, represented by the net area 
of the stress-strain loop for the cycle ; and (2) the giving out, during each cycle, of a 
_quantity of heat that produces a slight or moderate rise or gradient of temperature in 
the test-piece. Hysteresis may be measured mechanically or calorimetrically ; and 
experiments have shown that the quantities of work and heat are very approximately 
equivalent. 
When hysteresis is measured mechanically, by means of an extensometer or 
torsion meter used in conjunction with a suitable testing machine, the results are 
readily expressed in absolute units, but the degree of accuracy is unsatisfactory, because 
the hysteretic strains can be determined only by a process of subtraction involving the 
much greater elastic strains. Nevertheless, reliable measurements are obtained with 
moderate stresses, and sensitive instruments reveal definite hysteresis under very low 
stresses. The hysteretic work may be measured also by observing the decrements of 
a amplitude of a test-piece oscillating im vacuo ; and this method, many years ago, was 
‘used by Lord Kelvin in torsional experiments. 
Calorimetric measurements offer the advantage that the hysteretic energy may be 
‘measured directly—without reference to elastic effects—in terms of the rise or gradient 
- of temperature in the test-piece, which is considerable when a large test-piece is stressed 
ata high frequency. This method was first applied successfully with high frequencies 
in Prof. Hopkinson’s laboratory at Cambridge; and to the Cambridge group of 
investigators we are indebted for many interesting results regarding hysteresis. It 
was shown that the heat generated is very approximately equivalent to the work 
absorbed, and that this work is practically independent of the time occupied in 
making the cycle of stress, at least within wide limits from 0-01 second upward ; also 
‘that the actions in shear and in direct pull and push are very similar, and that the work 
per cycle varies as a function of the range of stress and is measurable down to very 
low stresses. It was further observed that hysteresis is much greater in annealed 
than in cold-worked metal; but this last conclusion requires important qualification. 
In these early investigations, however, attention was directed solely to the hysteresis 
exhibited in the earliest stage of fatigue tests, or to that observed in static tests ; and 
no attempt appears to have been made to follow its characteristic changes during the 
course of a complete fatigue test resulting in fracture after many million repetitions. 
‘In pursuance of the view that fatigue is closely associated with hysteresis, the author 
has carried out special experiments to measure hysteresis sensitively during the con- 
tinuance of tests that led-to fracture or, alternatively, left the test-piece still unbroken 
after many million cycles of stress. 
