COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 319 
therefore important to find out in what way the assumptions made in applying 
the theory are defective. 
Methods I. and II1., above, are subject to the usual assumptions of the 
mathematical theory of elasticity, namely, that the material is homogeneous and 
isotropic (or possesses some particular kind of xolotropy), that the stresses are 
proportional to the strains, and that the strains are so small that their squares 
may be neglected. As regards II., it has been shown that this method measures 
the stresses actually existing in the xylonite plates which are usually employed 
in the experimental work. Its use is therefore subject only to the assumption 
that the stress-strain relations of the material considered are of the same form 
as those of xylonite. 
In the first place, it is to be noted that method I. gives results which are 
in substantial agreement with those of method II. in those cases where a 
comparison is possible. We may therefore conclude that the assumption of 
linear stress-strain relations involves no important error provided the departure 
from linearity is of the same order as that of xylonite under the conditions of 
photo-elastic tests. Similarly we note that the assumption of infinitesimal strains 
is not material if the strains are comparable with those in xylonite under the 
‘above-mentioned conditions. Since xylonite exhibits, in these two respects, 
noticeable departures from the ideal assumptions, within the ranges of stress 
common in photo-elastic tests, it may be concluded that the effects of these 
assumptions are of little importance in practice except where relatively large 
strains occur, as in cleavage slipping and viscous flow. 
Further consideration of the causes of departure from theory may most con- 
veniently be made with reference to the type of fracture which occurs. For 
this purpose fractures may be classified as elastic or brittle, if rupture occurs 
without material inelastic deformation; plastic, if cleavage slipping occurs; 
viscous, if the type of fracture is mainly or largely determined by viscous 
flow; and fatigue fractures. The viscous type will not be further discussed 
here. 
i In the case of a member subjected to a steady load such that the fracture. 
when it occurs, is of the plastic type, it has long been known that stress concen- 
trations have little or no weakening effect. The reason for this is also well 
known, namely, that an amount of plastic flow, at the point of high stress, which 
is small compared with the amount of flow at fracture is adequate to annul the 
stress concentration. In some experiments described in a recent paper (4), the 
author showed that this flow occurs at approximately the estimated load even 
in the case of extremely small surface scratches having a depth of the order 
of 10-4 inch. 
The two practical cases in which weakening due to stress concentration is of 
real importance are those of elastic fracture under a load steadily applied, and 
fatigue failure under a periodically varying load. 
Much work has been done during the past few years which bears, directly or 
indirectly, on the question of stress concentrations in these two cases, and it 
may now be said with considerable confidence that one reason for the frequent 
discrepancy between the estimated concentration factor and the observed weaken- 
ing is, in both instances, the existence of a scale effect. The general result is 
that stress concentrations are practically unimportant if the linear dimensions 
of the region of high stress are sufficiently small, no matter what the estimated 
value of the concentration factor may be, provided that it does not exceed a 
certain high upper limit. As we have seen, this scale effect is not predicted 
by the purely theoretical methods of attack. 
As regards elastic fractures, the scale effect appears, so far as existing 
knowledge goes, to be the only important cause of observed departures 
from theory. In the case of fatigue fractures, on the other hand, it may 
be regarded as probable that redistribution of stress due to cleavage slipping 
often occurs under ranges of stress within the fatigue limits of the material. 
Under these circumstances an additional factor is introduced into the 
problem. 
_ The existing evidence on the above points is discussed in the three succeed- 
Ing sections. 
