320 REPORTS ON THE STATE OF SCIENCE, ETC. 
5. Seale Effect: (a) Elastic Fractures. 
With certain exceptions, combined stress tests which result in elastic 
fractures, and which do not involve stress concentrations, may be regarded as 
satisfying the law that rupture occurs when the greatest (positive) tensile stress 
reaches a particular value. The exceptional cases are those in which the greatest 
principal compression is numerically much larger than the greatest principal 
tension. 
Confining ourselves in the present discussion to cases where the greatest 
compression is not predominant, it appears that we may reasonably infer that 
the weakening effect of, say, a scratch should be obtainable at once from the 
tensile stress concentration factor. It is found, however, that this prediction 
is by no means verified if the scratches are small. 
A familiar illustration is met with in the operation of glass-cutting, where 
local weakening is produced by means of a scratch, the object being to determine 
the direction of fracture when the glass is subsequently broken. It is found 
that the weakening effect is insufficient unless the depth of the seratch exceeds 
a certain value, notwithstanding the fact that the estimated concentration factor 
due to the shallower scratches would appear to be quite adequate for the purpose 
in view. 
As an example of the same phenomenon in elastic fractures of crystalline 
metals, some experiments on.hardened cast-steel may be cited. 
The theory states that if surface scratches be made on a tensile test piece 
there should be no stress concentration in the case of scratches whose direction is 
parallel to that of the tensile stress, while if they are perpendicular to the direc- 
tion of the stress the concentration factor should be a maximum for the particular 
shape of scratch. Experiments were therefore undertaken,! at the author’s 
request, to find the effect of the orientation of the surface scratches on the tensile 
breaking load of dead hard cast-steel test-pieces. The scratches were made 
with No. 0 carborundum cloth, and their depth was of the order of 10-4 inch. 
The shapes of scratches made by this means were examined micrographically, 
and it was deduced that the concentration factor due to the perpendicular 
(circumferential) scratches should be 3 to 4 at least. In the tensile tests, 
however, there was no systematic difference between the breaking loads of the 
axially and circumferentially scratched specimens. Here, then, is a case of a 
severe stress concentration which appears to have been completely annulled by 
reason of the scale effect. 
In another experiment, conducted to determine the effect of larger grooves 
on the same material, two strips 0.025 inch thick and 0.5 inch wide were broken 
by bending. One of the strips had a serrated edge, the depth of the serrations 
being 0.025 inch. It was found that the breaking couple of the plain strip was 
2.48 times that of the serrated one. The concentration factor due to the 
serrations was estimated to be 2.9, so that in this case the greater part of the 
theoretical weakening was developed. 
A theory of scale effect in relation to elastic fractures was advanced by the 
author in the paper already mentioned (4). It was shown that, on the usual 
assumptions of elastic theory, the accepted strengths of materials, under tests 
which result in elastic fracture, are incompatible with strengths which are 
deducible on theoretical grounds from other physical properties of the 
materials, the theoretical strengths being by far the greater. A detailed investi- 
gation performed on a certain kind of glass indicated that this discrepancy could 
only be explained by supposing that the material contained minute flaws which 
gave rise to very severe stress concentrations. It was found that in this glass 
the necessary order of magnitude of the flaws was about 10-4 inch. In the case 
of vitreous materials a process was discovered whereby these flaws could be 
temporarily eliminated, and the substances then possessed tensile strengths 
agreeing approximately with the theoretical values. Thus for the particular 
kind of glass which was chiefly used the tensile strength was normally about 
25,000 lb. per sq. in. After treatment values as high as 900,000 Ib. per sq. in. 
were recorded, so that the concentration factor due to the flaws was about 36. 
These results suggest immediately an explanation of the scale effect. If a 
1 By Mr. W. D. Douglas, of the Royal Aircraft Establishment. 
