Simulations of the Localized Necking and Lüders Band in Irradiated Metals by Crystal Plasticity

In metallic materials, necking instability is initiated by underlying perturbations including surface imperfections or material inhomogeneity, and further facilitated by microstructural evolution. In this paper, the geometrical perturbation method and irradiation-dependent constitutive relationship are combined to simulate the occurrence of localized necking and the Lüders band with and without irradiation effects. Considering the necessity of perturbation in the simulation of deformation localization, the competition between extrinsic geometrical imperfections and intrinsic microstructure evolution on the necking process is revealed by a series of simulations with different perturbation coefficients. Moreover, face center cubic (FCC) metals including copper and austenitic stainless steel are taken as examples to correlate the irradiation hardening with the irradiation-advanced necking instability. The increase of flow stress and the decrease of work hardening capacity take responsibility for the limited ductility whereas the potential irradiation-accelerated texture softening is not observed. Then, a coupled mechanism of dislocations unpinning followed by the hindrance of movement is proposed to explain the increase of both lower yield point and Lüders strain in the irradiated mild steels, and a modified power law is used to depict the evolution of the Lüders band by simulations in which yield drop, stress plateau, strain transfer and strain hardening can be produced. The irradiation-induced diffuse necking is also present in pure metals for the first time by simulations. Our findings elucidate the important roles of geometry on necking instability and better reveal the clear physical picture of macroscopic deformation instability commonly observed in irradiated metals.