36 ME. LEONARD BAIRSTOW ON THE ELASTIC LIMITS OF 



and the two elastic limits are more conveniently referred to as "superior" and 

 " inferior " respectively, compression being regarded as negative stress. 



All the possible cases in which a material may be subjected to cyclical variations of 

 stress are covered by the following theory : 



" The superior limit of elasticity can be raised or lowered by cyclical variations of 

 stress, and at the same time the inferior limit of elasticity will be raised 

 or lowered by a definite, but not necessarily the same, amount. The range of 

 stress between the two elastic limits has therefore a value which depends only 

 on the material and the stress at the inferior limit of elasticity. This elastic 

 range of stress is the same in magnitude as the maximum range of stress 

 which can be repeatedly applied to a bar without causing fracture, no matter 

 how great the number of repetitions." 



BAUSCHINGER found that these definitions did not apply to the elastic limits as 

 measured on a previously unstrained specimen, and he made experiments to show 

 that the elastic limits in this case, which he called the " primitive " elastic limits, 

 were unstable, and that only a few reversals of stress were necessary to produce a 

 condition in which the theory was satisfied. 



In this latter state of the specimen BAUSCHINGER defined the elastic limits as 

 " natural " elastic limits. 



Other researches on fatigue to destruction have been described frequently.* Most 

 of these consider only reversals of stress between approximately equal inferior and 

 superior limits numerically, with an important exception in the original tests by 

 WOHLER. These tests and the machines used are fully described by Prof. UNWIN, 

 and it will be found that for the three materials most carefully investigated by 

 WOHLER sufficient information is given for a curve to be obtained by plotting the 

 minimum stress as abscissa and the corresponding safe ranges as ordinate. This was 

 done by GERBER, who showed that a parabola agreed to a first approximation with 

 the experimental results plotted in this way. If BAUSCHINGER'S theory is correct, 

 this parabola must also approximately represent the elastic ranges obtained under the 

 same conditions. BAUSCHINGER'S observations, however, so far disagreed with 

 WOHLER' s that he finally rejected GERBER'S parabola as untenable. 



Microscopic examination, as furnished by the experiments of EWING and 

 HUMPHREY,! supported BAUSCHINGER'S theory in" the case of equal and opposite 

 stresses. On the other hand, preliminary experiments by Dr. STANTON and the 

 author did not confirm BAUSCHINGER'S observations. 



* "On a Throw Testing Machine for Reversals of Direct Stress," 0, KEYNOLDS and J. H. SMITH 

 Phil. Trans.,' A, vol. 199, p. 265; F. ROGERS, 'Journal Iron and Steel Institute,' vol. Ixvii. (1905), 

 p. 491 ; T. E. STANTON and L. BAIRSTOW, " On the Resistance of Iron and Steel to Reversals of Direct 

 Stress," ' Min. Proc. Inst.C.E.,' vol. clxvi. (1903-6), part iv. 



t "The Fracture of Metals under Repeated Alternations of Stress," J. A. EWINO and J. C. W. 

 HUMPHREY, 'Phil. Trans.,' A, vol. 2t)0, p. 241, 



