The influence of the equilibrium stress growth law formulation on the modeling of recently observed relaxation behaviors

Abstract

Novel and consistent relaxation behaviors have recently been found with several steels at homologous temperatures less than 0.5, on a Titanium alloy, on an Aluminum alloy and on the polymer Nylon 66 at room temperature. A strong dependence of the relaxation rate on prior loading rate was observed. At equal relaxation times the stress at the end of the relaxation period associated with fastest (slowest) prior strain rate has the smallest (largest) magnitude. It is shown that the stress rate term in the evolution law of the equilibrium (back) stress enables the viscoplasticity theory based on overstress (VBO) to naturally model this newly found relaxation behavior. If the stress rate term is absent, as is the case for other state variable theories, this relaxation behavior cannot be modeled without modifications. Analyses valid at the beginning of and during the relaxation tests and numerical experiments illustrate the properties of VBO and other "unified" state variable models at low and high homologous temperatures.