322 REPORTS ON THE STATE OF SCIENCE, ETC. 
its fatigue strength, a conclusion which is not borne out by the results of 
tests. 
Another view was put forward by the author (4), according to which it was 
considered that the slipped surfaces suffered no permanent change, and that the 
amorphous phase was generated entirely at the inter-crystalline boundaries. On 
this theory, no phase change, and therefore no fatigue cracking, can result from 
cleavage slipping within a crystal unless the slipping extends at least as far 
as the junction with neighbouring crystals. Hence this theory, unlike the other 
two, does predict an effect similar to the observed scale effect, and to that extent 
is more satisfactory. It does not seem likely, however, that the author’s theory 
will prove entirely adequate in its present form, as many new and so far un- 
explained facts have come to light since the publication of the paper in which 
it was first advanced. For instance, some data now available suggest on the one 
hand that fatigue fractures can sometimes occur without cleavage slipping, and 
on the other that repeated cleavage slipping in certain materials does not neces- 
sarily lead to fatigue failure even though it extend over a number of crystals. 
On the experimental side the position of this branch of our subject appears 
to be even less satisfactory than on the theoretical side. So far as the author 
is aware, very few published results exist which are sufficiently complete for a 
close comparison with theory ; essential data, such as the shape of the scratches 
or the size of the crystals, being omitted. 
7. Fatigue Fractures: Effect of Stress Redistribution. 
It may be regarded as proved that, in many metals, no important plastic flow 
occurs, within the fatigue limits of stress, under an applied load alternating 
between numerically equal positive and negative values. Under these conditions 
the only uncertainty in applying the theory of stress concentrations is that due 
to the scale effect. 
The case is otherwise, however, in the technically commoner examples of 
fatigue failure in which the alternating load is superposed on a relatively large 
steady load. Fatigue under such loads is, in general, preceded by plastic flow, 
and in dealing with failure.at a point of local high stress, such flow involves a 
redistribution of stress in the neighbourhood. The nature of this redistribution 
cannot at present be found by calculation. It follows that while the range of 
stress at the fail point is calculable the mean stress is not; there is therefore 
no basis on which the ordinary data regarding the fatigue strength of the material 
can be employed to find the conditions of rupture at a point of stress concentra- 
tion under such kinds of load. 
In the case of some metals, some recent experiments suggest that plastic flow 
may be met with even under a pure alternating stress. 
It may be remarked that the effect discussed above, though a serious obstacle 
to theoretical work, is probably of great value in practice, since the redistribution 
of stress must decrease the mean stress, and therefore the weakening effect of fhe 
concentration. 
An additional complication accrues from the fact that if appreciable plastic 
flow occurs at the fail point the material there must be in a cold-worked condition, 
whence increased resistance to fatigue is to be anticipated. 
8. Stress Concentration in Mechanical Testing. 
It is customary, in the usual mechanical tests, including fatigue tests, to make 
the working portion of the test-piece of smaller section than the portions which 
are gripped, in order to localise the fracture and other effects of the test. The 
junction of the two parts is rounded off so as to secure a gradual change of 
section. Now, at such a change of section there must, in general, be a stress 
concentration, so that the actual maximum stress must be greater than the 
estimated working stress in the specimen; moreover, it is not usually possible 
at present to calculate the magnitude of the concentration factor. It appears, 
then, that if the difference between the estimated stress and the true maximum 
stress is appreciable the ostensible results of the tests may be materially 
erroneous, especially in the case of fatigue tests. 1t is evidently necessary in any 
Important test work to reduce this unknown factor to negligible dimensions. 
Partly on theoretical grounds and partly as tne result of experience with test 
