Plastic Behavior of Metals and Their Sensitivity to Grain Size: Comparison between Two Multiscale Approaches

This study evaluates two multiscale models to determine their ability to describe the effect of grain size (GS) on the plastic behavior of ultrafine-grained (UFG) and nanocrystalline (NC) materials. One model follows the Hall–Petch type (Model-1), while the other adopts dislocation kinematics to illustrate the grain boundary effect (Model-2). The stress–strain relation was utilized to present predictions about how various copper and nickel grain sizes affect the evolution of their plastic behavior. These predictions were compared to each other and their respective experimental databases. The copper databases stem from a well-known published paper, while the nickel databases were sourced from a research project. An analysis was conducted to evaluate each model’s ability to replicate the critical value (d_crit) for the UFG to NC transition. In the case of copper, both models produce a comparable d_crit of 16 nm. Model-1 has a lower sensitivity to yield stress below this value compared to Model-2. Both models accurately describe the weakening phase of metals below d_crit, particularly Model-2. The maximum error of 11% for copper was observed in Model-1, whereas Model-2 predicted a minimum error of 0.6%.