Effect of the rate dependence of nonlinear kinematic hardening rule on relaxation behavior

Relaxation experiments for metallic materials and solid polymers have exhibited nonlinear dependence of stress relaxation on prior loading rate; the relaxed stress associated with the fastest prior strain rate has the smallest magnitude at the end of the same relaxation periods. Modeling capability for the basic feature of relaxation behavior is qualitatively investigated in the context of unified state variable theory. Unified constitutive models are categorized into three general classes according to the rate dependence of kinematic hardening rule, which defines the evolution of the back (equilibrium) stress and is the major difference among constitutive models. The first class of models adopts the nonlinear kinematic hardening rule proposed by Armstrong and Frederick. In this class, the back stress appears to be rate-independent under loading and subsequent relaxation conditions. In the second class of models, a stress rate term is incorporated into the Armstrong–Frederick rule and the back stress then becomes rate-dependent during relaxation condition even though it remains rate-independent under loading condition. The final class proposed here includes a new nonlinear kinematic hardening rule that causes the back stress to be rate-dependent all the time. It is shown that the apparent rate dependence of the back stress during relaxation enables constitutive models to predict the influence of prior loading rate on relaxation behavior.