A Multiscale Approach For Tailoring The Macro-Properties of Polycrystalline Materials

Abstract

The first half of this thesis provides a continuum approach for predicting the constitutive response of HCP polycrystals using a simple non-hardening constitutive model incorporating both slip and twinning. This has been achieved by considering a physical based methodology for restricting the amount of the twinning activity. A continuum approach is used in modeling the texture evolution that eliminates the need for increasing the number of discrete crystal orientations to account for new orientations created by twinning during deformation. The polycrystal is represented by an orientation distribution function using the Rodrigues parameterization. A total Lagrangian framework is used to model the evolution of microstructure. Numerical examples are used to show the application of the methodology for modeling deformation processes. In the second half, the quantification and propagation of uncertainty in process conditions and initial microstructure on the final product properties in a deformation process is presented. The stochastic deformation problem is modeled using a sparse grid collocation approach that allows the utilization of a deterministic simulator to build interpolants of the main solution variables in the stochastic support space. The ability of the method in estimating the statistics of the macro-scale microstructure-sensitive properties and constructing the convex hull of these properties is shown through examples featuring randomness in initial texture and process parameters. A data-driven model reduction methodology together with a maximum entropy approach are used for representing randomness in initial texture in Rodrigues space. Comparisons are made with the results obtained from the Monte-Carlo method.