376 REPORTS ON THE STATE OF SCIENCE, ETC. 
must be kept below this yield-line, since otherwise the metal will yield before fatigue 
can develop. In the thin plates used in the experiment buckling would occur if 
the minimum stress (S — A) became compression. Hence, as a second limitation 
in this instance, the stress-point must be kept below the line OZ, whose equation is 
A=S8S. Combining these two theoretical limitations based on the yield stress and 
non-reversal, we see that the stress-point must keep within the 45° isosceles triangle 
OTY, of which the apex T is the intersection of the loci OZ and YY’ which run at 
right angles to one another. 
For a low tensile steel such as that used in the experiments, the ‘ basic’ fatigue 
limit is about 45 per cent. of the ultimate strength, say 10 tons persq.in. = Ay. Thatis, 
when § = zero, fatigue can occur only if A exceeds this value Ay. This point, marked 
Tons per Sy. Inch. 
0 5 My Is, 20 U 25 
(7492.6) Tons per Sg. Inch, 
Fic. 9 
on the axis of the diagram, is joined to the ultimate strength point U by two graphs : 
the one a parabola (Ay, Gerber, U) and the other a straight line (Aj, Goodman, U). 
According to Gerber and to Goodman respectively, fatigue can occur under different 
combinations of S and A only when the stress-point lies above the one or other locus 
respectively. Thus the metal is liable to fatigue when, and only when, 
A> Ao(1—(s/u)?), 
where the index 2 is to be taken as 2 according to Gerber, or 1 according to Goodman. 
It will be observed that, in the scale diagram fig. 9, even the Goodman locus lies 
wholly above the triangle OTY, indicating that fatigue should not occur under the 
limiting conditions explained above. The Gerber locus lies still farther above this 
limiting triangle; and accumulated evidence! indicates, at least for mild steel as 
used in practice and in this investigation, that the Gerber locus is the more correct 
of the two. It appears, therefore, improbable that fatigue can occur under stresses 
within the yield range, unless these stresses reverse in direction—acting as pull and 
push alternately. This conclusion has been verified in an experiment (A) described 
below, using metal with a low value of the ‘ yield ultimate’ ratio; and a further 
experiment (B) on steel with a high value of this ratio serves to limit the sphere of 
application of the conclusion. 
In experiment A, the test-plate was 1} in. in width, narrowed to # in. for a length 
of 1 in. in the middle, and joined to the ends by smooth transition curves such as 
would cause no appreciable concentration of stress. A fatigue test was made with 
S = 64.and A = 6 tons per gq. in., as represented by the point P (fig. 9) just below 
the apex of the limiting triangle. After 2852 millions of cycles of stress the test- 
piece was still unbroken. The steady component was then increased to 7$ tons per 
1 Haigh, Brit. Assoc. Report of Stress Committee, 1914. 
