International Journal of Plasticity ( IF 6.490 ) Pub Date : 2018-10-05 , DOI: 10.1016/j.ijplas.2018.10.002 Rainer Schwab
Reducing the grain size ranges among the most powerful methods to manage both high strength and high toughness of metallic structural materials. However, below certain grain sizes (often around 1 μm) some metallic materials lose most of their tensile ductility. In uniaxial tensile straining and related tensile forming processes, necking is then initiated immediately after first yielding. This in turn leads to a complete loss of uniform plastic deformation, a severe drawback in the use of these materials. Here, a new macromechanical approach in combination with micromechanical considerations is used to explain this long-standing riddle in materials science and engineering. The approach is based on the yield point phenomenon and the stress state that necessarily develops at the Lüders fronts. Using a simple new material model and a novel strain hardening law, it is clearly shown, that below a critical grain size the necessary nominal stress to spread out a Lüders band may be higher than the tensile strength. This invariably leads to a special form of plastic instability and the complete loss of uniform plastic deformation. Micro- and macromechanical considerations, experiments, analytical calculations and extensive finite element calculations are combined in this comprehensive study and fit together well. Furthermore, many features of the yield point phenomenon (the upper and lower yield strength, the spreading out of simple and complex Lüders bands, the stress fluctuations within the Lüders region) and the Hall-Petch relationship may now be understood in a new consistent way.