48 MR. LEONARD BAIRSTOW ON THE ELASTIC LIMITS OF 



necessary to decide the question, as the effect of the rigidity of the testing machine 

 has not yet been fully investigated. In two instances, at least, low ranges of stress 

 have been traced to natural periods of vibration in the testing machine agreeing 

 approximately with the period of repetition. 



The fact that the hysteresis loop is not necessarily a sign of failure increased the 

 difficulty of giving numerical values to the elastic ranges. 



If the widths of the hysteresis loops are plotted as ordiuates, on a range of stress 

 base, it will be seen that the curve obtained is approximately a straight line, 

 particularly for the lower ranges of stress. This line produced backwards intersects 

 the axis of range of stress. As the ordinate is zero at the intersection, the hysteresis 

 loop must disappear, or, in other words, the specimen must be completely elastic. 



The actual prediction was complicated by the fact that the hysteresis loop did not 

 always attain a constant width for the range. In such cases the width of loop was 

 taken immediately after the preliminary change in " cyclical permanent set," shown 

 most clearly in the upper curve of fig. 1. 



In most cases the " rate of permanent extension " afforded a check on the result, 

 as the prediction could be made by substituting this "rate" for the "cyclical 

 permanent set " and using the same method of extrapolation. 



Even with the greatest care the uncertainty of the correction to be applied was 

 too great to allow of much extrapolation, and the earliest results were always obtained 

 as close to the limiting conditions as possible. 



The ranges of elasticity are given to the nearest |- ton per sq. inch, which is about 

 the limit of accuracy expected. 



The Yielding of Iron and Steel. The earlier portion of the permanent extension 

 is of considerable interest. Except for the case of complete reversals of stress, the 

 application of a range of stress slightly in excess of the safe range produced an 

 elongation of the specimen, whether the maximum stress was above the yield-point 

 or not. This is shown in fig. 6, where the information necessary has been collected 

 and expressed graphically. 



The ordinates are the maximum stresses applied to the specimen and the abscissa? 

 the corresponding permanent extensions during the adjustment of the superior elastic 

 limits to the maximum stresses. Starting with a new specimen, the line FEA shows 

 that, at a stress of 25 tons per sq. inch, no permanent extension was observed. When 

 the load was slightly increased, a sudden extension of about one-fifth of a millimetre 

 occurred, this being the well-known yield. Further increase of stress extended the 

 specimen still further, the changes being represented by a line which cannot differ 

 appreciably from BC. In producing the curve FEABC no cyclical variations of stress 

 are concerned, and the curve is identical with the usual stress elongation diagram 

 frequently taken during a tensile test. 



The experiment on the specimen of axle steel described in fig. 3 showed that under 

 cyclical variations of stress an extension, which was not measurable at the first 



