Some recent developments of the endochronic theory with applications

In this paper we presented a comprehensive review of recent developments of the endochronic theory of plasticity. The endochronic theory was first proposed by Valanis in 1971 with the aim of circumventing some of the difficulties associated with classical theories of plasticity, such as the concept of a yield surface and its motion in the stress space, criteria for unloading, hardening rules, etc. The theory is developed by using irreversible thermodynamics of internal variables. In the early version of the theory the intrinsic time was defined as a measure of length in strain space. This version is now called the simple endochronic theory. The derived constitutive equations have been applied with success to a number of problems of practical interest, e.g. cyclic response, cross hardening, cross ratcheting, etc. However, it has been shown by the first author that the simple theory leads to an unloading response which is not elastic at its onset. As a consequence infinitesimal hysteresis loops in the first quadrant of the stress-strain space are open, in disagreement with observed behavior in metals. Recently Valanis introduced a new intrinsic time scale which is a measure of length in the plastic strain space. As a result, a new model of endochronic theory has been developed which leads to closure of hysteresis loops in the small as well as the large. It is also shown that the new model predicts the existence of a yield surface. Hardening rules proposed in the classical theory of plasticity appear as special results. It is also shown that the constitutive equations derived from the new model are very powerful in their quantitative prediction of steady cyclic response under constant strain amplitude conditions. In the case of cyclic creep the theory predicts the dependence of cumulative axial creep on the plastic shear strain amplitude but that it overestimates the dependence of the latter on the number of cycles. At the present time we think that this difficulty cannot be overcome on the basis of an isotropic theory. This suggests a future area of investigation and application of the endochronic theory.