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Extensive experimental investigations at ambient temperature on commercial Nylon 66, PEI (Polyetherimide) and PEEK (poly(ether ether ketone)) have shown that the overstress model developed for viscoplasticity should be, in principle, capable of modeling for solid polymers the rate-dependent behavior, including creep, relaxation and cyclic motions. The viscoplasticity theory based on overstress was modified accordingly to allow for the modeling of typical solid polymer deformation behavior. Included are nonlinear rate sensitivity, curved unloading, significant strain recovery at zero stress and cyclic softening. The visco plasticity theory based on overstress for polymers (VBOP) is introduced in uniaxial formulation. It is shown that VBOP can be thought of as a modified standard linear solid with overstress-dependent viscosity and nonlinear, hysteretic equilibrium stress evolution. VBOP consists of a flow law that is easily adopted to cases where the strain or the stress is the independent variable. The flow law depends on the overstress, the difference between the stress and the equilibrium stress with the latter being a state variable of VBOP. The growth law of the equilibrium stress in turn contains the kinematic stress and the isotropic or rate-independent stress, two additional state variables of VBOP. The material constants of VBOP are determined for Nylon 66 at room temperature and various tests are simulated by numerically integrating the set of nonlinear differential equations. The simulations include monotonic loading and unloading at various strain rates, repeated relaxation, recovery at zero stress that is dependent on prior strain rate, and cyclic strain-controlled loading. Finally, the stress-controlled loading and unloading are predicted with very good results. The simulations and predictions show that VBOP is competent at modeling the behavior of Nylon 66 and other solid polymers.

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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 ArmstrongFrederick 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.

a b s t r a c tA phenomenological constitutive model for cyclic viscoplasticity is presented within the framework of unified state variable theory. The model utilizes three distinct parameters to account for the cyclic (isotropic) hardening: drag stress, isotropic stress and rate sensitivity parameter causing the back stress to be rate-dependent. With the help of a ratedependent format of the back stress, the constitutive model can reproduce positive, zero and negative strain rate sensitivity of the flow stress in a concise manner. The purpose of the paper is to investigate the influence of the three parameters on stress relaxation behavior and rate-dependent cyclic hardening concerned with the variation in strain rate sensitivity. The applicability of the model to monotonic and cyclic loading is validated by comparing the predictions with experiments of two stainless steels and an aluminum alloy reported in literature.