Contribution to Discussion of the Paper by P. G. Hodge jr.

Abstract

Professor Hodge has clearly brought out the value of the use of the Tresca yield condition and associated flow rule in obtaining solutions of boundary value problems of plastic flow. In terms of Lode’s variables, this flow criterion appears to differ considerably from the experimental results of Taylor and Quinney: Phil. Trans. Roy. Soc., Lond., Ser. A 230, 323 (1931), and for this reason in the past the Mises flow law has been preferred in theoretical work. However, some recent solutions based on the Tresca criterion have been checked experimentally (J. Foulyes and E. T. Onat, Tests of behaviour of circular plates under transverse load, Brown University Report DA—3172/3, May 1955) and have been found to give remarkable agreement with experiment. In the problem of a loaded circular plate, the characteristics change from radial lines to logarithmic spirals at a certain radius and such a change was observed in markings on the plate surface. It seems therefore that solutions obtained by this method are more satisfactory than had been anticipated. The reason for this may be due to concentration of the corresponding points in the Lode diagram in the region of the diagonal in problems of non-homogeneous stress and strain, due to the freedom of the strain rate vector at the corners of the Tresca yield hexagon. It would seem worthwhile to look into this, for as Professor Hodge has shown, this technique offers an extremely powerful means of solution of plastic flow problems, which will be the more valuable when the basis for its accuracy is better understood.