Double-grid method for modeling microstructure evolution.

摘要

The microstructure of materials, i.e. the size, shape and arrangement of grains, determines essentially the material properties such as mechanical strength, toughness, electrical conductivity and magnetic susceptibility. In general the desirable property of materials can be controlled and improved by understanding of microstructure evolution processes in grain growth controlled by grain boundary migration, and grain boundary diffusion. The process of grain growth involves both grain boundary migration (moving interfaces) and topological changes of grain boundary geometry, and it can not be effectively modeled by Lagrangian, Eulerian, or Arbitrary Lagrangian Eulerian finite element method when in addition the stress effect is considered. A double-grid method is proposed for modeling grain boundary migration under stress. In this approach, the material grid carries kinematic and kinetic material variables, whereas the grain boundary grid carries only grain boundary kinematic variables. The material domain is discretized by a reproducing kernel approximation with strain discontinuity enrichment across the grain boundaries. The grain boundaries, on the other hand, are discretized by the standard finite elements. This approach allows modeling of arbitrary evolution of grain boundaries without remeshing.