An experimentally informed grain boundary model in 2–D: Addressing triple junctions, mobility and invariance of misorientation

Abstract

A novel 2-D continuum model for grain boundaries is presented, incorporating experimentally obtained data on grain boundary energy variation with misorientation. The model is employed to simulate the idealized evolution of grain boundaries within a 2-D grain array, following the methodology outlined in a previous study by us (Syed et al., 0000) . The approach of the model involves representing misorientation in a continuum scale through spatial gradients of orientation, considered a fundamental field. Based on experimental findings, the dependence of grain boundary energy density on the orientation gradient is found to be generically non-convex. The model employs gradient descent dynamics for the energy to simulate idealized microstructure evolution, necessitating the energy density to be regularized with a higher-order term to ensure the model’s well-posedness. From a mathematical perspective, the formulated energy functional fits the Aviles-Giga (AG)/Cross-Newell (CN) category, albeit with non-uniform well depths, leading to unique structural characteristics in solutions linked to grain boundaries in equilibria. The presented results showcase microstructure evolution, and grain boundary equilibria, illustrating reorientation of grains in two dimensional space. Idealized features such as equilibrium high–angle grain boundaries (HAGBs), curvature-driven grain boundary motion, grain rotation, grain growth, and triple junctions that satisfy the Herring condition in our 2-D simulations are also demonstrated.