Modeling of the plastic deformation of nanostructured materials with grain size gradient

Many studies have shown that the outstanding mechanical properties of surface nano-crystallized (SNC) materials were primarily attributed to the grain size gradient (GSG) region on their surface in which the grain size was ranging from tens of nanometers to tens of micrometers. In the present study, a dislocation density-based theoretical model was developed to investigate the mechanical behavior of the mentioned SNC materials. The constitutive behaviors of metallic materials with grain size ranging from tens of nanometers to tens of micrometers were established first. Note that an additional dislocation dynamic recovery term, which is grain size dependent, was included in the present model to account for the decrease of work hardening due to grain refinement. In addition, the stress-driven strain growth observed in experiments has also been incorporated into the proposed model. The proposed quantitative continuum plasticity model was capable of investigating the role of GSG in tuning the strength, ductility and work hardening rate of SNC materials. Our theoretical predictions were in good agreement with the existing experimental results. Furthermore, it has been found that the thickness fraction of the GSG layer and grain growth have significant influences on the strength and ductility of SNC materials. Therefore, the proposed model can be employed to optimize the mechanical behavior in SNC materials by controlling the thickness fraction and grain size in the GSG region and grain growth.