Constitutive equations for cyclic plasticity and cyclic viscoplasticity

The cyclic constitutive equations developed and used at ONERA and LMT-Cachan are presented in detail in terms of a hierarchy of various models. Both the time-independent and the viscoplasticity versions of the equations are discussed, as well as their ability to describe correctly most of the experimentally observed effects under monotonic or cyclic loading, constant or variable temperature, including strain hardening and time recovery effects. The reported experimental data concerns stainless steels and have been published previously. Four other theories are then presented and compared in a systematic way. They include the Ohno-Kachi time-independent plasticity theory, two unified viscoplastic models by Walker and by Krempl and Yao, the new developments of the endochronic theory by Watanabe and Atluri. All these approaches show some similarities with the first one, especially i that concerns the non-linearity of kinematic hardening, which represents the key for describing the cyclic behaviour of metallic materials.