Mechanics of incompatible asymmetric grain boundary migration

TL;DR

This work develops a phase-field framework where grain boundary eigendeformation evolves via a constitutive flow rule, F = F^e F^{gb}, enabling elastic compatibility to govern boundary migration. The model derives a mechanical driving force with two components from strain-energy differences and incompatibility, producing migration thresholds, back-stress, defect-like remnants, lamination, and apparent mobility asymmetry without intrinsic mobility asymmetry. Through stabilization, symmetric/asymmetric boundary migration, and curvature-driven tests, the study shows that directional effects and complex boundary morphologies emerge from mechanical incompatibility and Hadamard compatibility constraints, linking mesoscale mechanics to atomistic disconnections. The framework offers a transparent mesoscale link between atomistic observations and continuum plasticity, providing a basis for predicting boundary-mediated deformation and extending to crystal-plasticity coupling in future work.

Abstract

Grain boundary (GB) migration governs microstructure evolution and can mediate plastic deformation through sliding or shear coupling. Numerous experimental and numerical studies have reported a wide range of behaviors associated with boundary migration, such as defect emission or mode switching. Notably, recent studies have reported directionally asymmetric migration rates under symmetric loading, attributing this behavior to intrinsically asymmetric mobility; however, a mechanistic mesoscale explanation for this behavior remains lacking. In this work, we introduce a constitutive flow rule for grain-boundary eigendeformation within a multiphase-field framework, in which interfacial shear evolves in response to its mechanically conjugate driving force through the phase field Allen-Cahn equations. The formulation systematically employs regularized grain boundary shear kinematics informed by crystallography, and enables elastic compatibility to modulate boundary motion. Migration thresholds, residual back-stress, and apparent directional asymmetry appear naturally as emergent mechanical behavior. Simulations of symmetric and asymmetric tilt grain boundaries under mechanical, synthetic, and curvature-driven loading reveal persistent defect-like residuals following incompatible migration, transitions from planar motion to lamination at large inclinations, and even "ratcheting" behavior. These results provide a mechanically transparent explanation for behaviors such as effective mobility asymmetry and establish elastic compatibility as a constitutive mechanism in mesoscale models of boundary-mediated plasticity.

Figures (12)

• Figure 1: Stabilization of a square inclusion by compatibility-induced back-stress. No initial eigendeformation is imposed, so the inclusion is stress-free at initialization. Parameter $\theta$ denotes the twin-boundary orientation relative to the inclusion, and "fac" scales the elastic contribution to the driving force. Increasing "fac" arrests motion preferentially at incompatible corners.
• Figure 2: Shear coupling of symmetric and asymmetric tilt boundaries.
• Figure 3: Shear-coupled migration of the STGB with a slightly perturbed interface. Intervals show $\eta_1 [-]$ and $\sigma_{xx} [\mathrm{MPa}]$ at intervals corresponding to the markers in \ref{['fig:results/Lamination/stress_strain']}.
• Figure 4: Shear-coupled migration of the ATGB $\phi=10^\circ$ boundary with a slightly perturbed interface. Intervals show $\eta_1[-]$ and $\sigma_{xx}[\mathrm{MPa}]$ at intervals corresponding to the markers in \ref{['fig:results/Lamination/stress_strain']}.
• Figure 5: Shear-coupled migration of the ATGB $\phi=20^\circ$ boundary with a slightly perturbed interface. Intervals show $\eta_1[-]$ and $\sigma_{xy}[\mathrm{MPa}]$ at intervals corresponding to the markers in \ref{['fig:results/Lamination/stress_strain']}.