11. Ductile Damage Behavior in Low-Cycle Fatigue for Polycrystalline Metallic Materials

This chapter provides the basic and necessary elements concerning the anisotropy induced by damage. Moreover, local mechanism effect on the damaged behavior will be demonstrated leading to exceed the scope of this chapter. So, it is convenient to present, discuss, and analyze these subjects. Understanding some physical phenomena related to plasticity and damage is important in modeling. Hence, the main objective is to describe accurately the overall cyclic plasticity behavior coupled with damage via constitutive relations.

A micromechanical model of damage initiation in low-cycle fatigue will be presented for describing notably the damage deactivation effect. Actually, it is considered that the damage is active only if microcracks are open, while damage affects the mechanical properties of polycrystals during its closure (inactive phase) differently. With the small strain assumption, the plastic strain and local damage variables are examined at the crystallographic slip system scale. The anisotropic damaged behavior, induced by activation/deactivation phenomenon, is modeled using a fourth-order damage tensor at the overall scale. Accordingly, the overall nonlinear behavior, notably the deactivation phase due to the microcrack closure under complex cyclic loadings, is of particular interest in this chapter.