COMPLEX STRESS DISTRIBUTION IN ENGINEERING MATERIALS. 317 
at any point is shown as an ordinate to a flat face of the test-bar. Experiment shows 
that, in general, this surface, if the test-bar is sufficiently short, is concave in the central 
portion, and only tends to become plane over the central portion if the length between 
the shoulders is sufficiently great, while for the enlarged ends it is convex, tending to 
flatness at a sufficiently great distance away from the central part, with two rather 
complicated saddle-shaped surfaces over the changes of section connecting the various 
portions. It therefore comes about that, if the specimen is sufficiently short, no part 
of the member is ever stressed in pure tension within the elastic limit by forces applied 
at the ends. It is also comparatively easy, with a transparent model, to determine what 
length, if any, is in pure tension by plotting the zero isoclinics in plane polarised light, 
which latter curves at once effect the separation of the parts in pure tension from those 
under complex stress. Although not strictly necessary, such results have been com- 
pared with complete surveys of stress intensity in a plate tension member, and these 
are found to unite in giving the same delimitations of areas of the plate under pure 
stress as is determined by the isoclinics, while, to demonstrate its practical importance, 
the length of the parallel part of the tension member has also been determined in a 
few cases for which no pure tension is possible. 
Thus, in the case of the flat specimen just described, it isfound that thereisno purely 
tensional stress in the central straight part if this is less than 0°32 in. in length, when 
the connecting curves are } in. radius, but this length is increased slightly with smaller 
arcs, and reaches its maximum value of 0:42 in. when the re-entrant angle is as sharply 
defined as it is possible to make it. 
Specimens of Circular Cross-section. 
The general effect produced by changing the flat member to one of circular cross- 
section of the same contour is probably to intensify all the variations of stress described 
above, for change of the cross-section becomes proportional to the square of the 
transverse dimensions, instead of to the first power, and it is therefore most likely that 
the local concentration of stress near the ends of the central parallel part is larger 
than before, while the complex stress has been shown experimentally to penetrate 
further into the central parallel part than in the corresponding plane case. This can 
be observed by surrounding a specimen of cylindrical shape and enlarged ends with a 
flat-sided jacket of corresponding but slightly larger bore in every part, so that the 
small space between can be filled with a liquid of the same refractive index as the 
specimen and its jacket. A plain cylindrical rod under tension shows a system of 
colour bands parallel to its axis, due to uniform stress in the varying thickness under 
view; but if the specimen has enlarged ends, these bands begin to curve towards the 
axis before reaching the enlargements, owing to complex stress, and it is therefore 
possible to obtain the length under pure tension, which is always found to be less than 
the corresponding plane case. 
In one case, for example, of a short cylindrical specimen of 2 in. gauge length taken 
from a Standard Specification, the central part has a diameter of 0°564 in. to give a 
convenient cross-sectional area with a parallel portion 2} in. long connected to enlarged 
ends { in. in diameter by curved profiles of { in. radius. A model in the flat shows that 
this gauge length is just sufficient, while a truly cylindrical shape shows that complex 
stress invades the gauge length for a distance of } of an inch at each end, so that a 
parallel length of 24 in. is required for a 2 in. gauge length. 
The Effects of Indentations in Tension Members. 
The reduction of ultimate strength in a tension test-bar, due to the effects of a 
centre punch mark or letter stamped upon it, is often evident from the failure of the 
piece at a section where this local injury occurs, but its influence naturally extends 
beyond its immediate neighbourhood. 
Even a comparatively small local pinch, such as that exerted by the screw points 
of an extensometer, may be serious, as the lines of principal stress are then distorted, 
although not nearly so much in practice as in the case shown by fig. 54, where the 
transverse pinch is one-third of the longitudinal load, and therefore indicates complex 
stress over a considerable field. In general, however, stress across the line of the pinch 
rises to a very considerable magnitude at the surface, as indicated by the experimental 
values shown in fig. 58, which are found to be in fair agreement with the theoretical 
expressions obtained by Professor Filon.? 
2 Appendix 5. 
