Ductile Materials under Combined Stress. 73 



duce may be plotted into a curve of which an example 

 is shown in fig. 1, which is reproduced from a diagram 

 (for Swedish iron) drawn automatically by a Wicksteed 

 testing-machine, the ordinates being loads and the abscissae 

 actual extensions in an original length of 7 inches. Up to 

 the yield-point the extension is very small, being about one- 

 thousandth part of the length of the specimen ; the final 

 elongation, however, w r as in this case 29 per cent, of the 

 original length. 



4. The Yield-point, rather than the idtimate, Stress the cri- 

 terion of strength. — A closer examination into the relation of 

 the stress and strain below the yield-point shows that they are 

 proportional to one another (Hooke's law), and it is upon 

 this proportionality, or rather upon a generalization of which 

 the above is a special case, that the theory of elasticity is based. 

 Now if over any portion of a body the yield-point of the 

 material is exceeded, the basis of our calculations is vitiated, 

 and the redistribution of stress and strain may be widely 

 different from the proposed distribution and lead to imme- 

 diate failure. For this reason the yield-point, rather than the 

 breaking, strength should be taken as the criterion of the 

 strength of a ductile material in simple tension. 



Further arguments to the same effect arise from Wohler's 

 experiments, in which he showed that the frequent repetition 

 of a stress slightly exceeding the yield-point stress will finally 

 cause rupture. The yield-point as the criterion of strength 

 is so far accepted in modern practice, that most specifications 

 of steel now call for a yield-point not lower than one half the 

 ultimate strength. 



5. Variations of the Ultimate and Yield-point Stresses: 

 Annealing. — Neither the ultimate nor the yield-point stress 

 for a material is quite definite. For the former, besides 

 depending upon the taking account of, or the neglect of, the 

 reduction of area due to drawing out, is affected by the rate 

 of application of the load ; in fact, the phenomena displayed 

 by ductile materials under stresses approaching their ultimate 

 value are rather the dynamics of a semiviscous fluid than 

 the statics of an elastic body. And the yield-point is affected 

 by mechanical treatment. 



If in a tension test, after the stress-strain curve has begun 

 to rise after passing the yield-point, the load be removed, the 

 specimen is to all appearance unchanged. Let it, however 

 be regarded as a new specimen and be tested : it will exhibit 

 a yield-point close to the greatest stress previously applied to 

 it ; but a continuance of the test will show that its capability 

 of extension has been diminished. Such false yield-points. 



