Challenges in developing a general constitutive relation for cyclic loading*

Abstract

Abstract Deformation of most metals and alloys is time-dependent and this dependency becomes more pronounced at temperatures exceeding a third of the material's melting point. Furthermore, the deformation response of a material to cyclic loading involves transients prior to stabilization. Some manifestations of the transient responses are: strain hardening or softening, loading sequence effect, strain-rate and strain-path history dependency, creep-plasticity interaction, strain ratcheting, among others. In addition, a constitutive model formulated in terms of macroscopic parameters must have a certain underlying microscopic rationalization. In this paper rate-dependent constitutive relations for an inelastic material are presented. This constitutive model is of a coupled nature, in the sense that the effect of prior creep on the subsequent plastic deformation and vice versa, are taken into account. Thus, the framework for these constitutive relations is based on the concept that any loading sequence can be predicted by two separate (elastoplastic and creep) but coupled models. A number of examples covering a wide range of cyclic loading types are presented.