Hydrostatic Pressure and Conditions of Rupture. 73 



grains produced by the flow as a basis for the raising of 

 the elastic limit, but in a perfectly amorphous substance like 

 glass, which shows no alteration of shape, we have evidence 

 of no such internal change to account for the increase in 

 strength. The experiment suggests a difference between the 

 mechanism of yield and the mechanism of rupture. One 

 can perhaps see why rupture should not occur in the case of 

 the glass cylinders, since there is no place for the fragments 

 to go to in the case of rupture, no way for the rupture to get 

 started. But the same considerations would seem to show 

 also no possibility of yield towards the centre. Yet yield 

 toward the centre does get started and rupture toward the 

 centre does not get started ; there must be some essential 

 difference between the two. 



These collapsing experiments also dispose of one other 

 criterion of yield or rupture, better treated by the third type 

 of test. This is the third criterion mentioned above, namely 

 that rupture or yield will occur when the extension in any 

 direction exceeds a critical value. If the strain is calculated 

 in a cylinder exposed to hydrostatic pressure over the 

 outside, the radial strain is found to be an extension at the 

 inner surface. In the case of the ductile materials which 

 flow toward the centre, this radial extension increases 

 enormously with increasing flow, always without rupture or 

 separation of the fibres in the direction of elongation. And 

 in the case of glass under 24,000 atmos, where there is 

 neither rupture nor flow, the elongation at the centre is 

 greatly in excess of the elongation at rupture in an ordinary 

 tensile test, and therefore in excess of the supposed critical 

 elongation. 



The third type of test is concerned with the rupture of 

 heavy cylinders by internal pressure. The ordinary theory 

 of the bursting or yield of cylinders under internal pressure 

 is well known. At the inner surface the stress is a pressure 

 on planes at right angles to the radius, and a tension on 

 planes including the axis and radius ; the corresponding 

 strain is a circumferential elongation and a radial com- 

 pression. At the inner surface the stress difference, the 

 principal stress, the principal strain, and the strain difference 

 all have their maximum values. On any theory of rupture, 

 then, rupture would be expected to start at the inner surface. 

 The precise value of the theoretical bursting pressure 

 depends on the criterion accepted for rupture. If the 

 principal stress criterion is accepted, rupture will occur 

 when the hydrostatic pressure is equal to the tensile 

 strength ; if the maximum elongation is accepted, t rupture 



