The extended elastoplastic constitutive equation is formulated by introducing both the elastic boundary and the damage concepts for cyclic plasticity phenomena under the macroscopically elastic stress condition. These concepts are introduced to describe a pure elastic responses and a progressive degradation of stiffness of materials. The extended model is applied for metals obeying not only isotropic but also kinematic hardening law, and the mechanical responses under cyclic loading condition are examined in detail.
The lifetime prediction of structures is one of a dominant factor to achieve an optimum design. Also, it is well known that cyclic loads produce failure of structural parts for values of stress lower than those obtained in monotonic tests. This phenomenon is so-called fatigue and is the main cause of failure of machine parts in service. Classical approaches to study these phenomena involve the characterization of total fatigue life to failure by using the stress amplitude-life (S-N) curves, while some studies are based on the fracture mechanics (c.f. Suresh, 1998; Toyosada et al., 2003). On the other hand, continuum description of cyclic plasticity deformation during the fatigue phenomena is also useful for its understanding. In order to simulate these mechanical fatigue phenomena represented by cyclic plasticity such as ratcheting the plastic stretching within a yield surface has to be described, whilst the plastic strain is induced remarkably as the stress approaches the yield stress. The traditional plastic constitutive equation, however, is capable of describing deformation behavior for the stress path only near the monotonic/proportional loading, since its inside of the yield surface is assumed to be an elastic state. Therefore, various constitutive models, which are categorized in the framework of unconventional plasticity (Drucker, 1988) premising that an interior of the yield surface is not the elastic domain, have been proposed up to the present.
