COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 377 
sq. in., giving a maximum of 134, and it was found that the test-picce yielded slowly 
but steadily. 
Referring to fig. 9, it will be seen that the increase in S from 64 to 73 puts the stress- 
point just above the yield-line TY. Thus the non-occurrence of fatigue in the first 
test and the occurrence of yield without fatigue in the second are both in agreement 
with the theory given above. 
To show that in steel having a high ‘yield ultimate’ ratio fatigue may occur 
under unidirectional stresses that do not suffice to cause elongation by yielding : 
In experiment B, a test, similar to the above, was carried out on a sample of 
cold-rolled steel with Y = 45-5, U = 46-1 tons per sq. in., corresponding to a ratio 
Y/U of nearly 99 per cent. In this case the apex-point T is given by S = A= Y/2= 
22-7 tons per sq. in. A fatigue test was made with S = 20 and A = 16, well within the 
ge 
‘ 
ES 
29 
& 
R 
& 40 
29 of § 
veo 
Tons per Sq. Inch 
Fig. 10 
triangle corresponding to OTY (fig. 10), and it was found that the test-piece grew 
quite warm and fractured after only 60,000 cycles of stress. The contrast between 
figs. 9 and 10 and the different behaviour of the two steels may be explained, in the 
first place, by the fact that the triangle OTY for the harder steel is relatively larger 
than for the soft one on account of the high ratio Y/U; and, in the second place, by 
the Goodman and Gerber lines being relatively lower for the hard steel because the 
ratio Ao/U is usually lower than the 45 per cent. value assumed for the mild steel. 
These experiments were made with the Haigh alternating-stress testing machine, 
on test-pieces shaped to secure uniform stress conditions and avoid concentrations 
at shoulders. In this machine the pulsations have a frequency of 2,000 per minute, 
and experiments have shown that the frequency of pulsation does not within wide 
limits appreciably influence the results of fatigue tests. 
The perforations for rivets in bridge members introduce stress concentrations of 
great magnitude in the metal. In certain simple cases the local concentration of 
stress round an opening may be investigated mathematically ; and the conclusions 
hold rigorously when the stresses lie wholly within the elastic range. Thus 
Dr. Suyehiro 2 has shown that for a circular hole in a plate of unlimited width the 
greatest stress occurs on a transverse diameter and is three times the mean intensity, 
and Professor Inglis * has extended the mathematical analysis to a variety of other 
openings. 
_ The most common form of perforation in steel structures is of course the circular 
hole, which is more or less perfectly filled by the rivet. The exactitude of fit and the 
proximity of adjacent holes unquestionably affect the distribution of stress and present 
conditions too complex for mathematical treatment. 
1 The Engineer, July 29, 1921. 
2 Engineering, September 1, 1911. 
3 Transactions Inst. Naval Architects, vol. 55, p. 219. 
