Integration of Microstructure-Sensitive Design with Finite Element Methods: Elastic-Plastic Case Studies in FCC Polycrystals

摘要

A new mathematical framework called microstructure-sensitive design (MSD) was recently developed and demonstrated to facilitate solutions to inverse problems in microstructure design, where the goal is to identify the complete set of relevant microstructures (defined as statistical distributions) that are theoretically predicted to satisfy a set of designer-specified criteria on anisotropic macroscale properties and/or performance. In this article, we describe our efforts to interface the MSD framework with the finite element (FE) modeling tools used typically by the designers. This new MSD-FE framework facilitates a rigorous consideration of microstructure in a broad class of mechanical problems involving elastic-plastic design and optimization. The main elements of this newly developed MSD-FE framework are presented in this article, and their viability is demonstrated through two design case studies involving structural components made from FCC polycrystalline metals. The microstructure design variable in both these case studies is the orientation distribution function (ODF). The first case study involves the minimization of the elastic J-integral in the design of a cylindrical pressure vessel. The second case study involves the maximization of the load-carrying capacity of a thin plate with a central circular hole and loaded in-plane tension, while avoiding plastic deformation. In both these case studies, elementary upper bound theories were utilized in obtaining the macroscale properties of textured polycrystalline metal. It was observed that the elastic and plastic anisotropy associated with crystallographic texture influenced strongly the overall performance of the components.