| It is well known that the flow or stress-strain curves of conventional polycrystals level up exhibiting a hardening behavior when the grain size is decreasing within the micrometer range. However, when the grain size enters in the 10-20 nm range, an inverse softening behavior is observed and the stress-strain curves may become softer than their micrometer counterparts. This behavior is analogous to the Hall-Petch (HP) and inverse Hall-Petch (IHP) observed for the yield strength, as well as for the activation volume and pressure sensitivity parameters discussed in a preceding article. Here we develop a physically-based constitutive model for interpreting the aforementioned size-dependent behavior of the flow curves, in comparison with experimental results for nanopolycrystalline and nanotwins materials. Despite of its simplicity, this is the first physically-based phenomenological model that can describe HP and IHP behavior for flow curves at the nanoscale. A deeper approach for capturing such behavior may rest on structural defect considerations; in particular, the evolution and interaction of the pertinent defect population (dislocations, disclinations, twins) that emerge at the nanoscale. A preliminary discussion of this approach, will also be given herein. |
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