Transition theory of elastic-plastic deformation, creep and relaxation

Abstract

The classical macroscopic treatment of problems in plasticity, creep and relaxation has to assume semi-empirical yield conditions like those of Tresca, Von Mises and creep-strain laws like those of Norton, Odqvist, Kachanov and others. This is a direct consequence of using linear strain measures, which neglect the non-linear transition region through which the yield occurs and the fact that creep and relaxation strains are never linear. Tresca pointed out that a transition state, which he called the mid-zone, existed, and Todhunter and Pearson have supported him. In this state the whole of the material participates, and not simply a line or selected region, as is assumed by classical theories. Sir Lawrence Bragg expresses this view when he points out that an element of a crystal, embedded in the matrix, should be pictured as being strained together with the whole mass of the metal, and hence the slip must take place by a whole intra-atomic distance. A recent numerical investigation on flow and deformation theories also shows that a continuous approximation through a transition state leads to a satisfactory convergent solution.