A phase field model of the effects of dislocation microstructure on grain boundary motion during recrystallization

TL;DR

This work develops a three-dimensional phase-field framework that couples dislocation-density evolution to grain boundary migration during recrystallization by deriving a defect-energy functional from a dislocation microstructure model. It captures multiscale dislocation patterns, including incidental and geometrically necessary walls, and reveals how spatial fluctuations in defect energy drive anisotropic, wavy grain boundary motion and facet formation. The simulations reproduce complex front morphologies and lattice-rotation patterns observed in experiments, linking microstructural heterogeneity to macroscopic recrystallization dynamics. The approach provides a principled path to extend to polycrystals and dynamic recrystallization, offering a quantitative tool for predicting grain growth in deformed materials.

Abstract

The internal energy associated with the defect microstructure of strongly deformed crystals provides an important driving force for grain boundary motion during recrystallization. Typical dislocation microstructures are strongly heterogeneous and this heterogeneity affects the motion of recrystallization boundaries. In this study, a phase field model for microstructure evolution encompassing the evolution of both dislocation densities and grain order parameters is formulated. The model is employed to generate typical dislocation microstructures exhibiting multiscale features such as incidental and geometrically necessary dislocation walls. It is then used to study the motion of recrystallization boundaries in the associated complex defect energy 'landscape'. Results are compared to experimental observations.

Figures (10)

• Figure 1: Micrograph showing the shape of a recrystallization boundary migrating into a heterogeneous microstructure of geometrically necessary and incidental dislocation boundaries; pure aluminum cold rolled to 50% thickness reduction at room temperature, the letters R and D refer to recrystallized and deformed, respectively, the colors indicate local lattice orientation; after moelans2013phase.
• Figure 2: Formation of cellular patterns in symmetrical multiple slip of a LiF single crystal; total dislocation density at different shear strains.
• Figure 3: Evolution of stress, slip system strains, and dislocation densities during deformation in symmetrical multiple slip; left: total dislocation density and resolved shear stress on the 4 active slip systems; center: shear strains on the 4 active slip systems; right: dislocation densities on the active slip systems; all variables are given as functions of the average shear strain $\langle \gamma \rangle = M \epsilon_{xx}$ where $M=2$.
• Figure 4: Dislocation arrangement in the [100] plane; top: total dislocation density, center: lattice curvature tensor component $\kappa_{32}$, bottom: lattice orientation profiles along black line; left: strain $\eta = 0.42 b\sqrt{\rho_0}$ (tensile strain 2.1%) , right: slip system strain $\eta = 1.21 b\sqrt{\rho_0}$ (tensile strain 6.07% ); the arrows in the right graph mark geometrically necessary dislocation walls.
• Figure 5: Lattice rotation patterns in planes perpendicular and parallel to the tensile axis, left: perpendicular plane, right: parallel plane; the colorscale indicates rotations towards the [110] pole as yellow-green and rotations towards the [111] pole as purple-blue.