Viscoplastic Constitutive Equation Describing Inelastic Behavior of Polymers under Reverse Loading
Mamoru MIZUNO and Yukio SANOMURA
Abstract:Viscoplastic constitutive equations for polymers that properly describe strong strain recovery appearing in reverse deformation are proposed. Constitutive equations were formulated by combining the kinematic hardening creep theory of Malinin and Khadjinsky with the nonlinear kinematic hardening rule of Armstrong and Frederick. In order to describe the strain recovery, the nonlinear kinematic hardening rule was modified. First, a loading surface was defined in a viscoplastic strain space. A loading-unloading criterion was then introduced using the loading surface. Moreover, a parameter was defined by the relationship between the loading surface and the current state of the viscoplastic strain, and the evolution equation of back stress was modified using this parameter, which is applicable in reverse deformation. In the present paper, two models are proposed: Model 1, which is the evolution equation into which an additional term was introduced in order to suppress strain hardening of the back stress, and Model 2, in which a coefficient of the evolution equation was modified in order to suppress the evolution of the back stress. Experimental results for polyethylene were obtained using the modified constitutive equations, and cyclic inelastic deformation in the uniaxial state was predicted. Finally, the validity of the above-described modification was verified, and the features of the constitutive equations and the deformation were discussed. Key Words:Viscoplastic constitutive equation, Polymers, Strain recovery, Unloading, Armstrong-Frederick model, Loading surface, Polyethylene, Cyclic inelastic deformation