116 Mr. J. J. Guest on the Strength of 



47. The Material and Shape of Tubes satisfactory . — Turning 

 now to the results of the tube-tests, reference to Table IV. will 

 show that the densities found were high, and that the values of 

 the moduli of elasticity are usual values for the various 

 materials, and certainly not low ; also inspection of various 

 stress-strain diagrams indicates that the relation is linear up 

 to a considerable fraction of the yield-point stress. For these 

 reasons the tubes may be taken as of sufficient excellence in 

 material and shape to afford results worthy of consideration. 



Few torsion-internal pressure experiments have been per- 

 formed, but a comparison of results obtained thus with the 

 results of those tests when somewhat similar stresses are 

 differently produced, will tend to cause confidence in the 

 experiments. The torsion-internal pressure tests are Nos. IV. 

 5, V. 7, VII. 4, X. 9, and XII. 12. 



48. The Elastic - limit Phenomenon. — The elastic - limit 

 phenomenon, it will be observed, is much decreased in a 

 repetition of a test, the observed strain at the yield-point 

 being less in the second test than in the first, although the 

 stress-strain curves within the elastic limit practically coincide. 

 To illustrate this point some of the tests bearing upon it have 

 been plotted out observation by observation ; in figs. 16 and 

 17 are two sets of tension tests, and in fig. 18 some torsion 

 tests. 



When, however, a test imposes upon the material stresses 

 of a different type to those of the preceding test, the elastic- 

 limit effect, which may have temporarily disappeared owing to 

 the similarity of the two preceding tests, is displayed to the 

 full. 



Copper seems, however, to harden so much under successive 

 tests, that the strains appear as a whole to lessen with the 

 amount of treatment. 



The elastic-limit effect also increases with the number of 

 times different stresses have been applied to the material, as 

 may be seen by comparing the stress-strain curves for tests of 

 the same type, but separated by a number of other tests. 

 Examples are represented in figs. 16 (tension) and 18 

 (torsion) . 



This phenomenon may indicate that the cause of failure 

 under comparatively low varying stresses, such as employed 

 by Wohler in his experiments, is due to gradual increase of 

 size of defects, initially very small ; and 1 think tends to show 

 that the elastic-limit phenomenon is due to the occurrence of 

 the yield-point over small localities. 



