An overstress elasto-viscoplasticity model for high/low cyclic strain rates loading conditions: Part I – Formulation and computational aspects

Abstract

Plastic deformations of metallic materials depend on the rate of loading or deformation, implying rate-independent constitutive theories cannot catch a realistic response of the material when the loading condition is not quasi-static. Considering the conventional rate-dependent algorithms, the description of irreversible deformations does not show a smooth transition of the so-called viscoplastic strain from the elastic domain to the viscoplastic domain. In fact, a sudden generation of irreversible deformation takes place whenever the stress state exceeds the macroscopic yield stress during loading. Moreover, some models that adopt the overstress concept are not suitable for the description of impact loadings, since they predict an unrealistic elastic response, implying that the material could bear an infinite load. The present paper adopted the overstress subloading surface theory, which overcame the previous drawbacks. The constitutive equations were modified to take into account the movement of the similarity centre with the viscoplastic deformations to extend the description of the rate-dependency of the material to cyclic loading conditions. Moreover, aspects of the finite step accuracy of the algorithm and the local convergence are discussed.