Numerical Modeling of Microstructure Evolution in Nanocrystalline Alloys—Grain Boundary Segregation, Solute Drag, and Mechanics

Nanocrystalline (NC) alloys hold significant promise as structural alloys due to their superior mechanical properties over the traditional coarser grained microcrystalline alloys. Often, there is an optimal range of mean grain size for most metals about which maximum material strength can be realized. In the context of NC alloys, stabilization of the grain size in this optimal range is one of the primary synthesis challenges. A large volume fraction of NC alloy microstructure is occupied by grain boundaries (GBs). Since GBs increase the internal surface energy of the system, during solidification and grain growth phases, there is a tendency to minimize GBs through grain coarsening. However, in NC alloys, phenomena like GB–solute segregation and solute precipitation are active and mitigate grain growth and thus stabilize the desired small grains. Numerically modeling these phenomena of GB–solute interactions, and the evolution of these stabilized GBs under mechanical load, is 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–GB segregation-related effects and its coupling with mechanics has not be considered in the literature. We present a three-dimensional, finite element method (FEM)-based, finite-strain phase-field formulation for modeling grain evolution and microstructure stabilization in NC alloys. Beyond the formulation and its computational implementation, 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.