A multi-physics model for the evolution of grain microstructure

Abstract: When a metal is loaded mechanically at high temperatures, i.e. above 300 $^o$C, its grain microstructure evolves due to multiple physical mechanisms. Two of which are the curvature-driven migration of the grain boundaries due to increased mobility, and the formation of subgrains due to severe plastic deformation. Similar phenomena are observed during heat treatment subsequent to severe plastic deformation. Grain boundary migration and plastic deformation simultaneously change the lattice orientation at any given material point, which is challenging to simulate consistently. The majority of existing simulation approaches tackle this problem by applying separate, specialized models for mechanical deformation and grain boundary migration sequentially. Significant progress was made recognizing that the Cosserat continuum represents an ideal framework for the coupling between different mechanisms causing lattice reorientation, since rotations are native degrees of freedom in this setting. In this work we propose and implement a multi-physics model, which couples Cosserat crystal plasticity to Henry-Mellenthin-Plapp (HMP) type orientation phase-field in a single thermodynamically consistent framework for microstructure evolution. Compared to models based on the Kobayashi-Warren-Carter (KWC) phase-field, the HMP formulation removes the nonphysical term linear in the gradient of orientation from the free energy density, thus eliminating long-range interactions between grain boundaries. Further, HMP orientation phase field can handle inclination-dependent grain boundary energies. We evaluate the model's predictions and numerical performance within a two-dimensional finite element framework, and compare it to a previously published results based on KWC phase-field coupled with Cosserat mechanics.