178 APPLIED MECHANICS 
If after each unloading an interval of a few hours is allowed before — 
the next application of the load, it is found that this has the effect of 
raising the yield point still higher. Ifa bar which has been overstrained 
be loaded below its yield point and the extensions measured with a 
delicate extensometer, it is found that the elasticity of the bar is very 
imperfect, but after a sufficient period of rest the elasticity is restored. 
The elasticity lost through overstraining a bar of mild steel may be 
quickly restored by immersing the bar for a few minutes in boiling water. 
Another effect of this heating is that the yield point is raised as much as 
it would be after a considerable period of rest. 
For further information on the above subject the student is referred 
to papers by Ewing in the Proceedings of the Royal Society, 1880 and 
1895, also a paper by Muir in the Phil. Trans. Roy. Soe., 1899. . 
169. Effect of Fluctuating Loads.—General experience, and direct 
experiments, have shown that when the load on a piece is made to vary 
over a given range a sufficient number of times, fracture may take place 
at a much lower stress than the piece would have originally stood under 
a static load. For example, in one of Wéhler’s tests on wrought-iron, the 
tenacity under a static load was about 23 tons per square inch, but when 
loaded and unloaded about 10 million times, the load in each case pro- 
ducing a tensile stress of 15°28 tons per square inch, the bar broke. In 
another test on the same material the stress was made to vary from 8°6 
tons per square inch in tension to 8°6 tons per square inch in compres- 
sion, and the bar broke when the number of repetitions of the load was 
about 19°2 millions. 
Wohler was the first to investigate in a comprehensive manner the 
effects of fluctuating loads on the strength of iron and steel. His 
researches, which were carried on for about twelve years, embraced 
loading and unloading, and also partial unloading in tension, repeated 
bending in one direction and also in opposite directions, repeated twisting 
in one direction and also in opposite directions.* ne 
Further researches on this subject have been conducted by Spangen- 
berg, Bauschinger, Sir Benjamin Baker, Dr. J. H. Smith and Professor 
Osborne Reynolds, Dr. Stanton, and others. The subject is still being 
investigated by a number of experimenters. 
The general result of the numerous experiments which have been 
made seems to be that the maximum stress at which fracture will ae 
in any particular case depends to a large extent on the range of : 
fluctuation of stress as well as on the static strength of the material. 
Various empirical formule have been constructed to express the rela- 
tion between the maximum stress at fracture after a very large number 
of repetitions of the load, the static strength of the material, and the — 
range of stress. One well-known formula is the following, given by 
Unwin in his “ Machine Design,” 
Frnax. = 30+ ff? —n&f, 
where /max. is the stress at which fracture will probably occur after a 
sufficiently large number of repetitions of the load, f is the static ultimate 
* For details of Wohler’s tests the student may refer to Unwin’s Testing of — 
Materials of Construction, and also to Engineering, vol. xi. (1871). 
