COMPLEX STRESS DISTRIBUTION IN ENGINEERING MATERIALS. 825 
3. Prof. Coker’s Experiments to Determine Distribution of Stress in Region of Flanges. 
Having established experimentally that flanges do not affect the determination of 
E, Lasked Professor Coker whether he would examine the distribution of stress in the 
region of the flanges of a test-piece under load. A xylonite test-piece was prepared to 
the dimensions of fig. 8, and Professor Coker kindly tested it in his apparatus. His 
results disclosed that there was no stress in the flanges except at the root, where there 
was a slight concentration of stress, which was, however, perfectly symmetrical, in 
consequence of which, as the bar extends elastically, the flanges move down without 
distortion, so that the distance between the flanges is an accurate measure of the 
elastic extension of the gauge length which they define. Professor Coker continued 
his researches to find the distribution produced by points. This, however, Professor 
Coker would probably like to discuss himself. 
III. The Impressed Conditions of Fatigue Tests. 
By A. A. Grirritus, D.Eng. 
In practice, the results of fatigue tests are almost invariably given in terms of 
ranges or limits of stress. For example, statements such as ‘ the superior and inferior 
limits of stress were maintained at +15 and —5 tons per sq. in. respectively’ are 
usual. Now, as a matter of fact, very few fatigue-testing machines are so arranged 
as to render it possible to maintain any fixed limits of stress in the test-piece. The 
only machines in common use which are designed for this purpose are machines of 
the Haigh type, imposing direct pull and push, of controlled magnitudes, on a uniformly 
stressed test-piece. In practically all other cases the stress can only be controlled 
indirectly by controlling the external loads (e.g. bending and twisting moments) 
applied to non-uniformly stressed test-pieces, or by imposing constraints on the 
deformation of the test-pieces. 
In all such cases, the expression of the results in terms of stresses depends on an 
application of the mathematical theory of elasticity, and consequently involves the 
assumption that both limits of stress lie within the range of proportionality. Modern 
researches have shown that this assumption is inadmissible in the case of the majority 
of common metals. It is usually found not only that one or both of the fatigue 
limits lie outside the limits of proportionality, but also that the extent of the deviation 
from proportionality is a function of the number of repetitions and of the previous 
history of the piece. 
It follows that the results obtained with the several types of machine now in use are 
not directly comparable; the stated stress limits are, in general, purely nominal, 
inasmuch as they do not represent stresses actually existing in the material. 
It is therefore necessary to classify machines according to the nature of the 
conditions imposed by the machine, with any given setting, on the parts of the test- 
Piece in which fracture occurs, and to avoid making direct comparisons between 
results obtained with machines belonging to different classes. It should be remarked, 
moreover, that the characteristics of the testing machine only determine the general 
nature of the ‘impressed conditions,’ as they may conveniently be called—their 
precise specification would require, in addition, a complete knowledge of the stress- 
strain relations of the material. 
The following broad classification of impressed conditions is suggested as a basis 
for such a classification of testing machines :— 
I. Specific strain. In this case the limits of strain are maintained constant by 
the machine, independently of any variations in the stress, due to the process of 
fatigue. 
II. Stress diminishing as strain increases. In this case the conditions are inter- 
mediate between I. (above) and III. (below). 
III. Specific stress. In this case the limits of stress are maintained constant 
independently of any variations in the strains, due to the process of fatigue. 
IV. Stress increasing as strain increases. 
Some well-known types of fatigue-testing machines may now be considered in the 
light of the foregoing discussion. 
In the Wohler rotating-beam machine, the bending moment at the place of ulti- 
mate fracture is kept constant. If a solid test-piece is used, a comparatively small 
part of the section is undergoing overstrain at any instant of time, so that the strain 
in that part is determined by the elastic deformation of the remainder under a constant 
