Mesoscale Simulation of the Evolution of the Grain Boundary Character Distribution

Abstract

A mesoscale, variational simulation of grain growth in two-dimensions has been used to explore the effects of grain boundary properties on the grain boundary character distribution. Anisotropy in the grain boundary energy has a stronger influence on the grain boundary character distribution than anisotropy in the grain boundary mobility. As grain growth proceeds from an initially random distribution, the grain boundary character distribution reaches a steady state that depends on the grain boundary energy. If the energy depends only on the lattice misorientation, then the population and energy are related by the Boltzmann distribution. When the energy depends on both lattice misorientation and boundary orientation, the steady state grain boundary character distribution is more complex and depends on both the energy and changes in the gradient of the energy with respect to orientation.

Simulations of anisotropic grain growth: Efficient algorithms and misorientation distributions

“…The numerical simulations described here show good agreement with the results of prior simulations [9,12,13,15] but allow for the accurate evolution of much larger grain boundary networks. These simulations show that the MDF evolves quite differently in the fiber texture and random texture cases.…”

“…The initial MDF (thin red bars) is approximately uniform in the fiber texture case. The MDF is seen to rapidly sharpen around zero misorientation, consistent with prior investigations [12,13,15]. For random texture, the MDF is initially the Mackenzie distribution.…”

“…It builds on the distance function-based diffusion-generated motion (DFDGM) approach [7], which was used in earlier work [4,5] to simulate long time isotropic (equal surface energy) grain growth with very large numbers of grains. The initial simulations presented demonstrate this method recovers previous results using KMC simulations [9,12,13] and front tracking [15,2]. Subsequent simulations demonstrate the importance of the surface energy-to-misorientation map in predicting the time evolution of the MDF and suggests a framework capable of explaining the different MDFs obtained in the fiber texture and random texture cases.…”

“…For randomly textured initial conditions, KMC simu-lations [9,12,13] show only slight evolution from the initial MDF, which is a Mackenzie distribution. In contrast, the strong single component texture and fiber textured simulations [12,13,15] demonstrate sharpening of the MDF about zero misorientation from an initially uniform MDF. We perform a number of very large-scale, well-resolved simulations in two spatial dimensions to (1) confirm the results of these other much smaller simulations and (2) to give an explanation for the dissimiliar character of these results.…”

“…In addition, the fiber texture case was studied by Holm et al and Kinderlehrer et al [15] (using front tracking, with a different misorientation to surface energy map). Both investigations observed the concentration of the MDF at zero misorientation.…”