Invited Lecture
Modeling 3-D grain boundary evolution driven by the five-dimensional grain boundary energy landscape

Grain boundary (GB) evolution plays an extremely important role in the mechanical, thermal and electronic properties of micro/nano-crystalline materials. While there have been numerous efforts focused on the mechanical behavior of stationary GBs, many important properties in materials deformation such as recovery, recrystallization, and grain growth necessitate a dynamic treatment of these internal interfaces. Many of these properties are highly dependent on grain boundary (free) energies, which display complex five-dimensional dependencies on the GB geometry. These dependencies are behind important physical phenomena such as faceting, loss of stability of triple junctions, slip transmission, etc. Here we present a three-dimensional generalization of the Kobayashi-Warren-Carter (KWC) grain boundary evolution model governed by a fully-anisotropic GB energy density that depends on the misorientation and inclination of the grain boundary (Admal et al. [2018]). The model is parameterized using grain boundary energy data from atomistic simulations making it truly predictive. Computing gradient flows of the KWC energy is highly nontrivial due to its singular diffusive nature. Inspired by the thresholding method of Merriman, Bence and Osher (Merriman et al. [1992]), we present a new computational approach for the time evolution of the KWC model that results in a decisive improvement in the computation compared to existing implementations. We show that the evolution of model polycrystals can differ dramatically depending on the type of GB energy functional utilized, with important potential implications on their mechanical response.

References:

Nikhil Chandra Admal, Javier Segurado, and Jaime Marian. A three-dimensional misorientation axis- and inclination-dependent Kobayashi–Warren–Carter grain boundary model. Journal of Mechanics and Physics of Solids, 2018. In review.

Barry Merriman, James Kenyard Bence, and Stanley Osher. Diffusion generated motion by mean curvature. Proceedings of the Computational Crystal Growers Workshop, 1992.