Design across length scales: a reduced-order model of polycrystal plasticity for the control of microstructure-sensitive material properties

Abstract

Development of techniques for the control of material properties of polycrystal materials that are inherently dependent on preferred orientations (texture) is addressed. To account for the infinite degrees of freedom of microstructural features, a model reduction on the micro-scale is introduced. Reduced-order models are developed to model the evolution of microstructure described by an orientation distribution function using a finite element discretization of the orientation space. This reduced-order modeling approach is based on the technique of proper orthogonal decomposition (POD) and the method of snapshots. Furthermore, novel design problems are introduced for the control of microstructure based on realistic polycrystalline plasticity. Specifically, a gradient based optimization framework is introduced using a multi-length scale continuum sensitivity method (CSM). The model reduction is extended to the sensitivity analysis and is a key element for the success of computational design of deformation processes. Numerical examples that highlight the benefits of the continuum sensitivity method and model reduction are presented. In addition, the potential of the presented techniques towards process design for obtaining desired material properties is demonstrated with the control at a material point of the elastic modulus in fcc copper. A desired distribution of the elastic modulus is achieved through an optimal selection of the velocity gradient.