ed 
COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 185 
matter how great the number of repetitions. Bauschinger made experi- 
ments to show that these definitions did not apply to the elastic limits as 
measured on a previously unstrained specimen, and he made experiments 
to show that the elastic limits in this case, which he called primitive elastic 
limits, were unstable, and that only a few reversals of stress were necessary 
to produce a condition in which the theory was satisfied. In this latter 
state Bauschinger defined the elastic limits as ‘“‘ natural elastic limits.”’’ 
It is interesting, here, to note that the ideas underlying Bauschinger’s 
theory had been published so long ago as 1848 by James Thomson * ; who 
wrote: there are ‘ two elastic limits for any material, between which the 
displacements or deflexions, or what may in general be termed changes of 
form, must be confined, if we wish to avoid giving the material a set, or in 
the case of variable strains, if we wish to avoid giving it a succession of sets 
which would bring about its destruction ;’ . . . these limits “ may there- 
fore, with propriety, be called the superior and the inferior mit of the 
change of form of the material for the particular arrangement which has 
been given to its particles; that these limits are not fixed for any given 
material, but that, if the change of form be continued beyond either 
limit, two new limits will, by means of an alteration in the arrangement 
of the particles of the material, be given to it in place of those which it 
previously possessed.’ 
There is now no doubt concerning the existence, for iron and steel, of 
elastic ranges such as those found and actually measured by Bairstow. 
Provided that these ranges, when once attained, are never exceeded, it 
may be regarded as quite certain that any number of cycles of any speed 
of alternation can have no destructive effect. (See Article ‘ Elastic 
Hysteresis ’ of this Report.) But in most cases, certainly with cycles of 
unequal + stresses, and most probably with equal + stresses, the elastic 
range is reached through a partially elastic period which is gradually ended 
by recovery and the attainment of elastic limits adjusted to the range of 
stress. Though it is improbable that these elastic ranges can be affected, 
either in range or position of range, by speed of alternation, yet it seems 
quite certain that the duration of the period and the number of cycles 
necessary for the adjustment may be very largely influenced by this speed 
(No. 43). It is not so certain that the range,of adjustment does not 
depend on the temperature of testing ; but experimental evidence on this 
point is wanting. Thus it is not quite certain that the elastic ranges found 
by Bairstow would have been exactly the same if the temperatures of his 
experiments had been different. ; 
Mr. Bairstow’s method of finding the values of the elastic ranges from 
his observations is one that leaves a little room for personal judgment ; 
but since he estimates the probable error of this process to be within half 
a ton per square inch, it is clear that the elastic ranges found were quite 
definite. , 
‘The identity of these elastic ranges with the limiting safe ranges of 
fatigue tests can hardly be said to be conclusively proved. But there is 
considerable evidence in favour of it, and it appears to the writer that this 
identity may be regarded as sufficiently well established. 
The term ‘natural’ elastic limit is in certain respects a little misleading. 
A piece of material of a definite composition and crystalline structure will 
ett Cambridge and Dublin Mathematical Journal. The paper is quoted by Kelvin 
in his Article ‘ Elasticity, 2Hncy. Brit., 9th ed. vol. vii., p. 800, § 19, but does not 
appear to be generally known; it has recently been pointed out by Prof. J. Perry. 
