COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 293 
Along the central line, for example, there is a gradual change from high to 
fow tensional stress p in the direction of pull, accompanied by a variable cross 
stress g, which latter has a maximum tensional value very near to the section 
where the width of the member begins to increase, but it soon changes sign 
and becomes a small cross compression stress, and ultimately vanishes when the 
stress in the larger section becomes a uniform tension. A map of the stress in 
the direction of the line of pull for this case is drawn to a distorted scale both 
horizontally and vertically (fig. 2), in order to show the distributions at sections 
one-tenth of an inch apart, and from this it will be observed that the greatest 
variations of stress occur at the contours, and in general within the region of 
complex stress the maximum stresses occur at the sides in the smaller section 
and along the axial line in the larger section. The type of stress distribution 
shown here does not, however, appear to persist beyond the elastic limit in 
ductile material, and the variations of stress shown in the figure probably tend 
to equalise, and hence fracture does not necessarily begin to take place at the 
point on the contour where the maximum stress is indicated. In brittle 
materials, however, where little change occurs in the type of stress distribution, 
it is found that fracture occurs very frequently at this cross section. This 
latter result, which is often ascribed, and generally erroneously so, to imperfect 
centering of the specimen in the testing machine, is therefore more probably 
explained by the facts of the distribution observed. 
Another fact which emerges from the experimental observations is the 
penetration of complex stress into the parallel part of the reduced section, and 
it is easy to show for this case, where the model is one of three-tenths scale of 
an Engineering Standards Committee test bar, that complex stress occurs for a 
distance of .185 in. within the parallel part, so that in a specimen of this size 
and contour, and a parallel part 0.37 in. long, there is no pure tension stress 
at any cross section between the enlarged ends except possibly the central one. 
In a geometrically similar test bar with connecting arcs of one inch radius 
it would appear, therefore, that a total length of 1.23 in. of the parallel part 
is in a state of complex stress, and since it is found experimentally that complex 
stress distribution at the ends does not vary to an appreciable extent as the 
length of the parallel part increases beyond this, it may be inferred that, within 
the elastic limit, a sufficiently short tension test member under load may be in 
a state of complex stress, which has little or no resemblance to pure tensional 
stress at any part of it, and it is therefore likely to give fallacious results for 
practical applications. 
In the example cited above the limiting length of the parallel part for which 
there is no pure tension stress across the sections between the shoulders is 
1.23 in., and for such a case complex stress occurs at all sections except 
possibly the central one. 
The danger of accepting tension tests on short specimens as representing the 
true behaviour of the material in pure tension is clear, especially as it is not 
difficult to show (2) that in turned specimens of the same contour as a flat bar 
specimen the complex stress in the former extends further into the gauge length 
than in the latter. 
In another standard form widely used in Continental practice the enlarged 
ends are gradually tapered towards the gauge length and have straight line 
contours, which join the parallel part at a very obtuse angle. At this junction 
vhoto-elastic observations show that there is a small amount of stress concen- 
tration probably not more than 10 per cent. greater than the stress intensity in 
the gauge length and. moreover, very localised in extent. 
In still another form, used by Professor Dalby, mainly to avoid contact 
stresses and local indentations of extensometer screws, the extremities of the 
gauge length are defined by two thin collars turned on the specimen with con- 
necting arcs to the main body of 0.04 in. radius. In this case the stress 
concentration is very local, and is rather more than 30 ver cent. (3) of the mean 
average stress, and is symmetrically disnosed with reference to the collar. It 
1s, moreover, practically indenendent of the radius of the fillet within wide 
limits, and in that.respect differs from the stress at a re-entrant angle, where 
ee cadius of the fillet is the main factor which determines the stress concen- 
ration. 4 8 ’ 
_ Observations Of stress distribution by photo-elastic means indicate, in 
Genvyal, Vhat the stress tontentrations desoribed Above tend to eqtallse more ot 
