COMPLEX STRESS DISTRIBUTION IN ENGINEERING MATERIALS. 331 
Further experiments are being directed to compare the actions of metals that may 
be expected to show greater and less degrees of local hardening, and in metals that do 
or do not exhibit primary hysteresis; and to investigate the actions of stress com- 
binations in which the ratio s : a differs in a wide range. 
In the meantime, the foregoing results are published to indicate how the dangerous 
effects of the stress-concentrations, though definitely less than those suggested by 
mathematical theory applied in the most direct manner, appear to be closely related 
to the results of mathematical analysis. 
REFERENCES. 
1 Suyehiro, Proc. Inst. N.A. 
2 Inglis, Proc. Inst. N.A. 
3 Filon and Coker, Report of B.A. Stress Committee, 1914, pp. 201-210. 
‘ Coker, Chakko and Satake, Inst. Hng. & Shipbdrs. in Scotland, vol. Ixiii. 
5 Wilson and Haigh, Report of B.A. Stress Committee, 1923. 
6B. P. Haigh, Report of B.A. Stress Committee, 1923. 
V. Note on the Distribution of Stress in Fatigue Test-Specimens 
(Torsion and Bending). 
By Professor W. Mason, D.Sc. 
Experimental work published in the Reports of the Committee has shown ! that 
stee] may endure cycles of alternating stress, reaching to 70 millions, with accompany- 
ing hysteresis of a magnitude incompatible with elasticity. Further work has 
demonstrated that the hysteresis of protracted alternating tests, at ranges certainly 
below the fatigue range but above the limit of proportionality (under increasing alter- 
nating loading), is many times greater than hysteresis which can be classed as ‘ elastic 
hysteresis.’ It must be admitted, therefore, that the portion of the Bauschinger 
theory which explains prolonged endurance, under equal plus and minus stresses, by the 
hypothesis of recovery or alteration of elastic limits, will not fit these new facts. The 
following fact appears to be established ; prolonged repetitions of a fatigue-limit 
range of stress induce, in mild and medium steel, a range of strain that remains extra- 
elastic, not merely with reference to any primitive condition, but inasmuch as it entails 
persistent ‘ cyclical permanent set.’ There is a hysteresis loop of comparatively large 
ratio of width to length which may persist, in the writer’s experience, over 100 million 
eycles. This cycle appears to be exactly reversible mechanically ; although, of course, 
it is not reversible thermodynamically. 
It is usual to calculate the stresses due to ranges of torque or bending by formule 
which are built upon the assumption of perfect elasticity. Error is of course entailed 
by use of these formulz, and the question arises as to the amount of this error. An 
interesting point that immediately presents itself is how far the stress and strain in a 
solid specimen are affected by the central core of elastic material ; whether this core 
exerts a constraining influence on the extent of the cyclic extra-elastic strain ; or 
whether, on the other hand, elastic breakdown is propagated into the core, producing 
therein a low value of the limit of proportionality; and arising from this is the ques- 
tion, which so far as the writer knows is unanswered, whether there is a ‘scale’ 
effect, i.e. whether the stress and strain distribution would be different for specimens 
of different diameters. An assumption of linear distribution of strain from axis to 
skin appears, however, to be justifiable on general grounds;? and on this basis the 
distribution of stress may be inferred from a comparison of alternating torsion tests 
on hollow and solid specimens. 
Calculations have been made by the writer for the following cases :— 
Alternating Torque.—The limits of the error entailed by the use of the usual formula 
ean be calculated with a considerable degree of precision, since the real stresses in 
hollow specimens with thin walls can be calculated within very narrow limits. The 
error entailed in solid specimens of mild or medium steel is between 10 and 13 per cent. 
for fatigue limits of stress. 
Alternating Bending (in one plane fixed relatively to the specimen of circular 
section).—The limits of the error have been calculated § and are wider than for alter- 
nating torque. The parts of the specimen affected by cyclic extra-elasticstrain are two 
small segments only of the circular area, which makes the calculation of the error 
