Three-dimensional computational modeling of polycrystalline materials

A method for modeling three-dimensional polycrystalline materials is presented in this dissertation. Models were constructed from measured serial sections using a reconstruction technique that maintains the grain boundary topologies and interfaces. An interface-respecting smoothing technique was used to reduce the artificial stair-steps, and an accurate and efficient decimation technique was used to simplify the bounding surfaces down to a size that is tractable on commodity computers. The smoothing and decimation routines were constrained to produce high-quality surface facets. The complexity of the microstructural models is high and significant mesh refinement would be necessary to employ the finite element method, but an enhanced natural element method presented here is capable at handling these models. Examples of residual stresses from processing temperature changes and internal stresses from mismatched grain orientations are presented in this dissertation.