Formulation of a new single crystal law for modeling the cyclic softening

The present paper proposes to modify the single crystal law [Hoc, T., Forest, S., 2001. Polycrystal modelling of IF-TI steel under complex loading path. Int. J. Plast. 27, 65–85] used in polycrystalline model developed by [Pilvin, P., 1990. Approches multiéchelles pour la prévision du comportement anélastique des métaux. Ph.D. Thesis, Université Pierre et Marie Curie; Cailletaud, G., 1992. A micromechanical approach to inelastic behavior of metals. Int. J. Plast. 8, 55–73], in order to account for the cyclic softening observed in some metallic materials during fully reversed low-cycle fatigue tests under total strain control. Experimental observations [Mayama, T., Sasaki, K., 2006. Investigation of subsequent viscoplastic deformation of austenitic stainless steel subjected to cyclic preloading. Int. J. Plast. 22, 374–390] show that the cyclic softening is partially due to a rearrangement of dislocations in hard and soft zones within the grains during cyclic straining. We propose thus to modify the initial single crystal law by including a composite model of hard and soft zones on each slip system within a grain. The softening is modeled through the evolution of soft zones. The model is applied to a FCC polycrystal. The self-consistent scheme is used in order to obtain the polycrystalline macroscopic behavior. The results show that the new model correctly describes an initial cyclic hardening, a subsequent cyclic softening and finally a stabilized state.