Theoretical effect of large hydrostatic pressures on the tensile strength of materials.

Any yield or fracture condition which is constructed from the deviator of the stress field will fail to account for the effect of hydrostatic pressure on the flow and fracture characteristics of a solid, as shown by Bridgman.' This criticism applies in particular to the von 1\iises and Tresca yield conditions which are widely used in the theory of plastic flow. To meet the above and other objections to the commonly accepted yield conditions, we have recently derived a simple invariant criterion for slip and subsequent fracture based on the general idea advanced by MNlohr, i.e., that the decisive role in the initiation of slip over a surface element in a solid is played by the interaction of the shearing and normal stresses on the element.2 It is the specific purpose of the following note to show that this slip and fracture criterion will satisfactorily explain Bridgman's results on the tensile strength of steel cylinders subjected to large hydrostatic pressures. Other materials tested by Bridgman appear to exhibit the same qualitative behavior as steel under hydrostatic pressure; but the data for these materials are not at present sufficiently extensive to permit a meaningful comparison between theory and experiment. In Tables 1 and 2 the first column designates the specimen by means of three figures as follows: the first figure shows the variety of steel, the second the heat treatment of the variety, and the third denotes the particular sample on which the test was made. The second column in each of the tables shows the hydrostatic pressure at the completion of the test, and the last column gives the measured tensile strength defined as the maximum load divided by the original cross section of the sample. The graphs in Figure 1 are based on the data in Tables 1 and 2 and are typical of the relationship between the tensile strength and the imposed hydrostatic pressure as shown by tests on a large number of different steels. The relationship between strength and pressure is linear to within experimental error