Spectral methods for modeling microstructure evolution in deformation processing of cubic polycrystalline metals

The mechanical properties of engineering materials are directly controlled by the underlying microstructure, which in turn is governed by the processing methods. The complete description of microstructure is extremely complex and is also not required for many microstructure-properties relationships of interest. The relevant details of the microstructure that influence strongly the elastic-plastic properties of the material include the lattice orientation distribution (texture), the grain size and shape distribution, and the arrangement and distribution of dislocation networks on the various slip systems in the constituent crystals. Of these, the crystallographic texture is perhaps the most important aspect of microstructure that has a strong influence on the elastic and the initial yield properties of most polycrystalline materials used in the manufacture of engineering components. It should also be noted that crystallographic texture is likely to have the dominant effect on the inherent anisotropy exhibited by these materials.The objective of this thesis is to provide a mathematical framework for the development of material databases; capturing the relevant details of the microstructure, while paying attention to inherent anisotropy of properties associated with them. Here crystallographic texture is the only microstructural parameter that is considered. This work is motivated by a new design paradigm called microstructure sensitive design (MSD) which employs statistical description of microstructure and its core feature is the efficient spectral representations of microstructure-property-processing linkages. Using the MSD framework as the basis, novel computational methodologies were developed in this work to build material spectral databases in single phase cubic polycrystalline materials. These databases were critically evaluated in three different cases: 1) To predict the effective macroscale elastic properties in perfectly disordered copper polycrystals 2) Evolution of the microstructure and the concomitant anisotropic stress-strain response during deformation processes in FCC polycrystals and (3) in developing a processing recipe to obtain a targeted texture using selected processing techniques.Ph.D., Materials Science and Engineering -- Drexel University, 200