Endochronic Rate-Sensitive Constitutive Equation for Metals, Application to Generalized Creep and Large Deformations

摘要

A constitutive equation is proposed with a view to describing the rate dependent mechanical response of metals at high temperatures. The equation is of the endochronic type and derives its physical foundations from deformation kinetics. Of importance is the fact that hardening is associated with a change in the energy barriers brought about by the inelastic deformation of a metal. The equation is used to describe the results, by Ohno and his associates, of experiments on the creep response of metals to piece-wise constant histories. The metal in the present case is 304 stainless steel at 600 degrees C. It is shown that the theory gives analytical results that are in agreement with experiment. Note should be made of the fact that the constitutive equation applies to general three-dimensional histories and is thus not limited to histories associated with creep. The theory is also extended to finite deformations. A constitutive equation is derived, using internal variable theory, to the effect that the Cauchy stress is quadratic functional of the relative Finger tensor and in terms of a time scale which is intrinsic. The precise definition of the time scale is given in the text. A number of important problems are solved in closed form under conditions of constant strain rate. The industrially important problem of the axial compression of a block is solved numerically. Keywords: Plastic properties.