Hydrostatic Pressure and Conditions of Rupture. 71 



unstable configuration of the molecules set up in the metal 

 by the overstrain. In the case of ordinary metals, where 

 hysteresis appears before the yield-point of the metal as a 

 whole has been reached, hysteresis is probably connected 

 with local yield in the neighbourhood of the larger or more 

 unstable crystalline complexes of the metal. 



The application of all this to theories of rupture is 

 immediate. It suggests, in the first place, that there is no 

 necessary connexion between the yield-point and the rupture- 

 point. Engineers, after some discussion, seem to have 

 accepted the yield-point as the best criterion of rupture. 

 The reason seems to be that the yield-point and the rupture- 

 point are fairly close together, the yield-point is pretty 

 definitely located, and it is possible to calculate the relation 

 between stress and strain up to the yield-point and so to 

 find a criterion at lenst for yield, if any exists ; whereas it 

 is well known that the usual relations between stress and 

 strain break down in the region of viscous flow between the 

 yield- and the rapture-points. Here, in these tests, there 

 is a yield-point but no rupture-point at all, so that certainly, 

 even if a criterion were found for yield, it could not be 

 extended to rupture. 



These tests further show that the maximum stress dif- 

 ference criterion of yield is no more valid than the maximum 

 stress difference criterion of rupture. For if the distribution 

 of stress in the cylinder be calculated on the maximum 

 stress difference hypothesis, it will be found that the hole in 

 the cylinder will never close up under any pressure, no 

 matter bow large. The mathematical solution of this 

 problem is given in another paper in which this whole 

 question of the collapsing of cylinders is taken up much 

 more in detail*. The solution assumes that the maximum 

 stress difference condition holds throughout the entire 

 extended process of yield. To account for the observed 

 complete closing of the hole it is necessary that the greatest 

 stress difference which the metal can support become less in 

 the last stages of yield. To inquire whether the initial yield 

 always occurs at a definite stress difference would be of little 

 avail, for it is well known, that even for the ordinary tests of 

 engineering the material must first be put into a state of 

 ease by subjecting it to considerable stress. If it is not so 

 subjected to preliminary stress, it may show yield or 

 departure from Hooke's law at values of the stress very 

 much lower than normal. But in tests of this type there is 

 no natural limit to the stress which shall be used to put the 

 * Phys. Review, xxxiy. pp. 1-24 (1912). 



