It appears that the material, just before fracture, is in an un stable state of stress. Any local contraction of area will cause an increase of stress in that region, and this in turn will cause fur ther plastic distortion, or "flow." On the other hand, the harden ing effect of plastic strain operates in the reverse direction, tend ing to increase the resistance to flow. It is probable that this second effect pre dominates in the earlier stages of the test, and so maintains stability; for it seems clear that the first effect, once it predom inates, must result in final rupture. The notion of instability seems to explain the observed fact, that the ultimate stress (at fracture) is largely dependent upon the form of the test specimen.
Rupture may occur by direct sep aration over a surface which is nearly plane and perpendicular to the direction of the pull: such fractures are characteristic of hard steels and other non-ductile materials. But in ductile materials, which break at a "waist," the fractured specimen generally reveals a ring-shaped crater on one side of the break and a truncated cone on the other (fig.
22) : rupture has occurred by shearing on the outer (inclined) surface and by direct separation in the central region, where the fracture is approximately plane.
Go. A question of great interest, both scientific and practical, is the effect of stresses which fluctuate repeatedly between definite limits. Hodgkinson, in 1837, first drew attention to this problem. At that time, bridges of masonry were being replaced on an ex tensive scale by bridges of wrought iron, and engineers who appreciated the significance of Hodgkinson's experiments realized that the properties of the new material were very imperfectly understood. A commission was appointed to consider the applica
tion of iron to railway structures, its report (1849) described experiments which indicated clearly (I) that failure can result from repetitions of a load less than the ultimate static load, and (2) that such failure is not caused by dete rioration of the material with time, if the ultimate static load may be taken as an indication of quality.
Fracture produced by a large number of repetitions of stress is generally described as "fracture by fatigue." The classical researches on the subject are those of A.
WOhler, who tested iron and steel under di rect tension, torsion and and who paid, for the first time, strict attention to the magnitudes of the local stresses involved. Wohler's experiments showed that a stress well below the ultimate strength of a material (as measured in an ordinary tension test) will suffice to produce fracture if it be often enough removed and restored, or even alternated with a smaller load of the same kind; the smaller the range through which the stress is varied, the greater is the number of repetitions (or stress cycles) which a specimen can endure.' These investigations have been continued by many other work ers, and the literature bearing on the subject of fatigue is now very extensive. Only the merest outline can be given here : the reader is referred to a very clear and complete account by H. J. Gough, The Fatigue of Metals (1924) Testing Machines.-6I. Many distinct types of machine have been devised for applying fluctuating stresses. Perhaps the most important is Wohler's "ro tating bar" machine, which (in the modified form employed at the National Physical Laboratory, England) is illustrated in fig. 25. The specimen, a solid or tubular rod, is rotated by an electric mo tor (as in a lathe) at speeds up to 2,400 r.p.m. It is subjected to equal up-and-down forces, ap plied through ball bearings, at two points in its length, by a small single-lever testing machine and by dead weights. Thus it is exposed, over the greater part of its length, to a uniform bending moment ; and since the plane of this bending moment rotates in relation to the specimen, the stress at any point in a cross-sec tion fluctuates between positive and negative values during each revolution. Within the elastic limit, the stresses can be calculated in accordance with § 30.