Numerical modeling of microstructure evolution in nanocrystalline alloys - grain boundary segregation, solute drag and mechanics

Abstract

Nanocrystalline (NC) alloys hold much promise as structural alloys due to their superior mechanical properties over traditional coarser grained microcrystalline alloys. Strength of metallic alloys is related to the underlying grain size - as represented by the classical Hall-Petch relation. Generally, a metals strength increases with decreasing mean grain size from the micrometer scale to the nanometer scale, until about a mean size of 20 nm. Any further decrease of grain size results in decreasing strength. Thus, there is an optimal range of mean grain size for most metals about which maximum material strength can be obtained. In the context of NC alloys, stabilization of the grain size in this optimal range is one of the primary synthesis challenges. Since nm-scale mean grain sizes are desired, phenomena like GB solute segregation and solute precipitation are utilized during alloy synthesis to mitigate grain growth. Numerical modeling the phenomena of GB-solute interactions and the evolution of these stabilized GBs under mechanical load are of immense interest to the NC alloy community. To enrich the numerical modeling formulations available in this space, we present here a phase-field method based numerical framework to model GB segregation, solute precipitation and effect of external loading on NC alloys. While some of these effects have been modeled in isolation, a unified treatment of the solute and GB segregation with mechanics interactions has not be considered in the literature. We present a 3D FEM finite-strain phase-field formulation for modeling grain evolution and microstructure stabilization. Beyond the formulation, various case studies demonstrate the applicability of this framework. Further, thermodynamic and kinetic arguments are provided based on the evolution of GB energy to explain the effects of solute drag, GB pinning and mechanical deformation.