Scott. — Resistance of Steel to Mechanical Shock. 517 



expected that if the stress engendered by a live load exceeded 

 the elastic strength of the material, failure must eventually 

 result from the accumulated plastic extensions; if, on the other 

 hand, the elastic limit was not reached, that the piece would 

 be safe. Many failures, however, occurred in which by no 

 method of computation could the material be shown to be 

 loaded above its elastic strength. 



This apparent anomaly led Wohler and subsequentlv Bau- 

 schinger and others to investigate the effect of repeated and 

 alternating stress, or, in other words, of " fatigue," on materials. 

 These investigations have resulted in establishing that the 

 " physical constants " of a bar are the cumulative result of its 

 " life history," and that its elastic limit may be artificially raised 

 by overstrain or cold rolling, but that such an elastic limit is 

 exceedingly unstable, and may be reduced to a very low value, 

 or even zero, by heating, hammering, or alternation of load- 

 ing. It can be seen, therefore, that failures by repeated loading 

 within the nominal elastic limit may be explained by the as- 

 sumption that the limit was an unstable one. 



Further, Wohler and Bauschinger found that with gradu- 

 ally applied repetitory or alternating loads the range of stress 

 which the bar is worked over is the principal factor in its en- 

 durance — the smaller the range, the greater the load which can 

 be carried — and that the relationship between the statical 

 breaking-strength (t), the breaking-strength when the load is 

 altogether removed and again reapplied an unlimited num- 

 ber of times (u), and the breaking-strength when the load is 

 completely reversed (to the same magnitude but opposite sense) 

 an unlimited number of times (s), is t : u : s : : 3:2:1. 



Many formulae have been devised to fit the results of these 

 experiments. Gerber showed that if the minimum stresses were 

 plotted as abscissa?, and the corresponding limiting ranges of 

 stress as ordinates, the points fell upon the curve of a parabola. 



On the basis that many of Wohler' s experiments gave the 

 ratio of t : u : s : : 3 : | : 1, Launhardt and Weyrauch con- 

 structed equations, the former for the limiting ranges of re- 

 petitory, and the latter for the limiting ranges of alternating, 

 loading. These formulae have been very generally used, but 

 on plotting the results given by them it will be found that the 

 curve is non-continuous, there being a change of direction at 

 the one stress zero-point. There are also other anomalies. 



Some years ago the writer discovered that if the more cor- 

 rect values of the relationship of t, u, & s of t : u : s : : 3 : 2 : 1 

 be adopted, the equations of Launhardt and Weyrauch reduce 

 to the common form of 



a = \ t[ 1 + i-r — ) 



3 V 2 L max./ 



