2020/06/28 by Julien Fausty, J. Fausty, Fausty, J. +12
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Anisotropy #Boundary (topology) #Boundary value problem #Computational Engineering #Convergence (economics) #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Finance #Finite element method #Geometry #Grain boundary #Grain growth #Grain size #Materials Science (cond-mat.mtrl-sci) #Materials science #Mathematical analysis #Mathematics #Mechanics #Metallurgy #Metallurgy and Material Forming #Numerical methods in engineering #Physics #Thermodynamics #Work (physics) #and Science (cs.CE) #cond-mat.mtrl-sci #cs.CE #math.DG
paper · pdf · doi:10.48550/arxiv.2006.15531
published in arXiv (Cornell University) (Cornell University)
arxiv created 2020/06/28 · openalex publication_date 2020/06/28 · arxiv updated 2020/06/30 · openalex created_date 2020/07/02 · openalex updated_date 2026/08/06
Grain growth in polycrystals is one of the principal mechanisms that take place during heat treatment of metallic components. This work treats an aspect of the anisotropic grain growth problem. By applying the first principles of thermodynamics and mechanics, an expression for the velocity field of a migrating grain boundary with an inclination dependent energy density is expressed. This result is used to generate the first, to the authors' knowledge, analytical solution (for both the form and kinetics) to an anisotropic boundary configuration. This new benchmark is simulated in order to explore the convergence properties of the proposed level set finite element numerical model in an anisotropic setting. Convergence of the method being determined, another configuration, using a more general grain boundary energy density, is investigated in order to show the added value of the new formulation.