Polycrystal plasticity modeling of deformation microstructures

In this thesis, deformation microstructures of face-centered cubic materials are simulated and studied using finite element methodologies. The polycrystal models consist of rhombic dodecahedral shaped crystals, each finely discretized with tetrahedral elements. The rhombic dodecahedron, a twelve-sided, regular, space-filling polyhedra, is used to represent a microstructure with equiaxed grains. Polycrystals are constructed by assembling dodecahedra in regular arrays. Material behavior is based on rate-dependent, crystallographic slip which is restricted to a limited number of slip systems. A number of numerical investigations are subsequently performed on this model polycrystal.; The influence of the local neighborhood on crystal deformation is examined by conducting a series of numerical experiments on the same set of crystals. Each simulation uses a different spatial mapping of orientations to effectively alter the neighborhood of each crystal, allowing the dependence of deformation on crystal orientation to be examined. Comparisons are made to earlier results obtained with brick shaped crystals and to the results obtained with a second polycrystal consisting of a very fine discretization. Coarse crystal discretizations are adequate for modeling bulk anisotropic properties, but a detailed investigation of local neighborhood effects require a finely discretized mesh that is better able to capture gradients in the deformation field.; Spatial deformation variation present in polycrystals can lead to grain subdivision characterized by the formation of boundaries separating regions with differing lattice orientation. Particular attention is focused on the resulting crystallographic misorientation across these boundaries and their orientations relative to the applied loads. This evolving intra-grain boundary texture is compared to published experimental data obtained using TEM and Kikuchi pattern analysis. Strong correlations between the simulated model and experimentally observed material are observed.; In addition, two novel hybrid finite elements over tetrahedral domains are introduced, providing the foundation for the modeling of anisotropic incompressible materials. The low-order mixed elements provide a stable, invariant three-field method for preserving the incompressibility constraint. Stability is ensured by enhancing the velocity field with bubble functions. Least-order, invariant stress fields are obtained via group theoretical arguments. Tetrahedra provide a greater flexibility than the more common brick-type elements in meshing complex 3D domains and are typically the staple of automatic meshing software.