Subloading surface model in unconventional plasticity

Abstract

For engineering problems, the elastoplastic constitutive model has been required, which is applicable to the prediction of cyclic loading behavior for various stress/strain amplitudes. The subloading surface model has been proposed and developed in order to respond to this requirement. he original subloading surface model (or the bounding surface model with a radial mapping) does not assume a yield surface enclosing an elastic domain in which stress rates of any direction do not induce a plastic deformation. Instead, it assumes a normal-yield (or bounding) surface and a subloading surface which always passes through a current stress point in not only loading but also unloading states retaining a geometrical similarity to the normal-yield surface. Thus, it describes a continuous stress rate-strain rate relation in a loading process, bringing about a smooth elastic-plastic transition, and its loading criterion does not require the judgement whether a current stress lies on a yield surface or not. It cannot, however, describe reasonably an induced anisotropy and a hysteresis behavior for a stress change within the normal-yield surface, since the center of similarity of normal-yield and subloading surfaces is fixed or the translation rule is not formulated reasonably. In this paper an exact formulation of this model is presented by deriving a translation rule of the center of similarity and a consistency condition for the subloading surface and by examining the physical meaning of the loading criterion in terms of a strain rate and the associated flow rule concurrently for materials with an anisotropic hardening/softening and without an clastic domain. It is capable of describing an anisotropic hardening/softening, a smooth elastic-plastic transition and a hysteresis behavior including Masing effect, a closed hysteresis loop and a mechanical ratchetting effect consistently. This model is described for metals and is compared with test data of the torsional cyclic loading behavior of stainless steel.