COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 321 
small surface scratch be formed whose depth is of the same order as the 
dimensions of the flaws already existing, but which gives rise to a less severe 
stress concentration, the strength of the piece must clearly be unaffected, since 
whether the scratch be present or not, rupture must be occasioned by the stress 
concentration due to the flaws. If, however, a groove be made, of such a size 
that the region of high stress is large compared with the size of the flaws, there 
must be a double magnification of stress, arising firstly from the concentration 
of stress at the bottom of the groove, and secondly from the flaws within that 
region of high stress. 
Since the above-mentioned paper was published, it has been found possible 
to prepare pure vitreous silica in a stable form in which a relatively large pro- 
portion (at least one-third) of the theoretical tenacity is retained. According to 
the theory, this implies that the flaws must be reduced almost to molecular 
dimensions, whence it follows that the scale effect should be practically non- 
existent. 
This conclusion has received ample support from a number of experiments, 
the results of which are sufficiently illustrated below. 
Two thin circular rods of the material were touched together as lightly 
as possible, whereby a minute injury, invisible under a magnification of 
250 diameters, was inflicted on the surface of each. One of the rods was broken 
by flexure, with the abrasion on the tension side. The degree of flexure at 
rupture was only about one-eighth of that required to break an uninjured rod 
of the same diameter. ‘lhe other rod was broken with the injury on the com- 
pression side, and in this case no weakening could be detected. This is in 
agreement with the hypothesis of rupture under a specific tensile stress, since no 
concentration of tensile stress should arise from a surface defect on the com- 
pression side of a bent beam. Further experiments were performed in which 
rods were lightly touched with other solid bodies, both hard and soft, and with 
the finger tip. In all cases a notable weakening resulted. Even if a rod was 
left exposed to bombardment by the dust particles in the atmosphere there was a 
slow but perfectly definite weakening. 
In the case of brittle substances, then, it appears that stress concentrations 
due to minute flaws and surface defécts, far from being negligible, constitute 
the controlling factor which determines the magnitude of the technically avail- 
able tenacity of these materials, a result which may be regarded as a remarkable 
vindication of the elastic theory of stress concentrations. 
6. Scale Effect: (b) Fatigue Fractures. 
The general nature of available experimental results in this branch of the 
subject is the same as in the case of elastic fractures, that is to say, fine scratches 
appear to have little or no effect, while sufficiently large grooves often give rise 
to nearly the full theoretical weakening. The evidence is, however, less com- 
plete, and much more work is required to place our knowledge of scale effect in 
tatigue phenomena on a satisfactory basis. 
On the theoretical side the main difficulty arises from the lack of a well- 
established theory of fatigue phenomena in general. Beilby’s original work (5) 
on the production of an amorphous phase in metals by overstrain showed that 
large internal stresses might be set up as a result of cleavage slipping, by reason 
of the difference in density between the amorphous and crystalline phases. This 
result suggested as a possible theory of fatigue that the internal stresses set up 
by repeated cleavage slipping, when combined with the stress system externally 
applied, might ultimately be adequate to initiate a brittle fracture of the material. 
Beilby considered that the amorphous phase was developed between the slipped 
surfaces, so that on the theory derived from his work fatigue fracture should 
always be an ultimate effect of repeated slipping. A similar conclusion may be 
reached regarding the theory of Ewing and Humfrey (6), according to which 
fatigue cracks are initiated by the attrition of the slipping cleavage surfaces. 
A difficulty in connection with both these theories is that, as the present 
author has shown (see §4 above) cleavage slipping can occur at the corners of 
very small scratches at loads very much below those necessary to cause it to take 
place in the remainder of the material. According to the foregoing theories, 
therefore, the presence of such scratches on a test-piece should greatly reduce 
