Nonlinear anelastic behavior and unloading-reloading constitutive models of severe plastic compressive deformation

Abstract

The nonlinear anelastic behavior in unloading and unloading‒reloading processes of severe plastic compressive deformation (SPCD) has a decisive impact on the springback of deformed parts. The strain hardening, strain softening and anisotropy affect the anelastic behavior of the deforming material. In this study, the quasi-static single-pass and multi-pass SPCD tests were carried out on the samples along different directions of hot-rolled copper plates. The nonlinear unloading behavior and the variation law of anelastic strain after single-pass and multi-pass compressions and between passes were analyzed, and the effect of the anisotropy on the anelastic strain was clarified. At the micro level, the anelastic strain model in the strain hardening and softening stages was established based on the relationship between anelastic strain and dislocation density, the Hall-Petch and Talor strength models, strain hardening EM model and modified softening constitutive model. Thereby, the nonlinear unloading‒reloading models in an anelastic exponent form and in a modified anelastic hyperbolic sine form were constructed, respectively. At the macro level, the anelastic strain function related to strain were established on the basis of the chord modulus model in a power exponent form and strain hardening and softening constitutive models. Thereby, 1-D ET nonlinear unloading‒reloading constitutive model in a power exponent form was constructed. The nonlinear symmetric relationship between unloading and reloading curves was analyzed. It was found that the 1-D ET model in power exponent form and expression in polynomial form can accurately describe the instantaneous slope of symmetric axis. Finally, the anelastic strain and the unloading‒reloading curves of the single-pass and multi-pass SPCDs and inter passes were predicted using the anelastic strain model and the nonlinear unloading‒reloading model, and compared with the experimental results. The comparison indicated that the established anelastic strain model can accurately predict the anelastic strain in the strain hardening and softening stages of SPCD, and the established unloading‒reloading model can accurately predict the nonlinear relationship between stress and strain in the unloading‒reloading of SPCD.