Modeling the elastic and plastic response of single crystals and polycrystalline aggregates

Understanding the elastic-plastic response of polycrystalline materials is an extremely difficult task. A polycrystalline material consists of a large number of crystals having different orientations. On its own, each crystal would deform in a specific manner. However, when it is part of a polycrystalline aggregate, the crystal has to ensure compatibility with the aggregate, which causes the response of the crystal to change. Knowing the response of a crystal enables us to view the change in orientation of the crystal when subjected to external macroscopic forces. This ability is useful in predicting the evolution of texture in a material. In addition, by predicting the response of a crystal that is part of a polycrystalline aggregate, we are able to determine the free energy of each crystal. This is useful in studying phenomena like grain growth and diffusion of atoms across high energy grain boundaries. This dissertation starts out by presenting an overview of the elastic and plastic response of single crystals. An attempt is made to incorporate a hardening law which can describe the hardening of slip systems for all FCC materials. The most commonly used theories for relating the response of single crystals to that of polycrystalline aggregates are the Taylor model and the Sachs model. A new theory is presented which attempts to encompass the Taylor as well as the Sachs Model for polycrystalline materials. All of the above features are incorporated into the software program "Crystals".