Hydrostatic Pressure and Conditions of Rupture. 79 



hoops. One might expect, then, to be able to reach a 

 pressure abont twice that of the yield-point under pure 

 tension, but as a matter of fact it is possible to exceed this, 

 because of the hardening of the metal by over strain. Thus 

 a copper cylinder, originally ^in. i. d. and 3 in. o. d. has been 

 subjected to 10,000 atmos. without the yield extending 

 throughout the entire mass. The inner hole has been 

 stretched about 50 per cent, by this pressure. Pressures of 

 30,000 atmos. have been reached in cylinders of soft nickel 

 steel or of tool steel, and of 40,000 in a cylinder of hardened 

 nickel-steel. But the hardening process by over load is not 

 nearly so complete or thorough as it is for cylinders collapsed 

 by external pressure. The yield under high pressures con- 

 tinues for a very much longer period of time, and the raising 

 of the elastic limit after complete disappearance of set is not 

 permanent. After a period of rest, yield is likely to begin 

 again at a pressure lower than the former maximum. Thus 

 a cylinder of soft nickel-steel, originally 8 in. o. d. and |- in. 

 i. d., had had the elastic limit apparently raised to 28,000 

 atmos. by repeated applications of pressure which stretched 

 the inner hole from | in. to 1£ in. But now, after several 

 years of use, it is unsafe to subject this same cylinder to 

 more than 15,000 atmos. The initial yield-point of the 

 cylinder was about 8000 atmos. 



Summary. 



In this paper the results of three types of tests with high 

 hydrostatic pressures have been described in their bearing 

 on theories of rupture. The tests of cylinders under pressure 

 on the curved surface only (" the pinching-off-effect ") show 

 that the maximum principal stress criterion is not valid. 

 The tests of hollow cylinders under external pressure show 

 that neither the maximum shear stress nor the maximum 

 shear strain criterion is valid, while the tests on the bursting 

 of heavy cylinders under internal pressure show that the 

 maximum elongation criterion is not valid. These conclusions 

 apply to both brittle and to ductile materials. The tests do 

 suggest that there may be some essential difference between 

 a ductile and a brittle material (more generally between a 

 crystalline and an amorphous one), but show that the 

 distinctions proposed hitherto cannot hold. It is suggested 

 that in every case there must be some more general condition 

 satisfied than those usually considered. There is not enough 

 material at hand to enable a formulation of the condition to 

 be made, but the considerations with regard to the bursting 



