SUMMARY

The principle concern of the material scientist is the connection between microstructure, properties, and processing. Microstructure is characterized via experimental measurements of geometry at the appropriate length scale. This is usually followed by a quantification of microstructure via statistics for which there are a broad base of possibilities including classical stereological measures such as grain size and higher order descriptions like the N-point spatial correlations. Despite advances in 3D characterization of microstructures such as X-ray tomography and serial sectioned SEM, most techniques still capture measurements only in 2D sections. Even when 3D datasets are available they are typically measuring only small volumes leading to uncertainty about their statistical significance. Can we build statistically representative reconstructions of 3D microstructure from the partial information gathered on a collection of 2D cross sections? The proposed work introduces new approaches to these problems for polycrystalline metals and other materials with complex geometries. Efficient algorithms for the computation of "higher order" statistics, such as N-point correlations and chord length distributions, will be explored. These higher order metrics will form the basis for establishing structure based representative volume elements (RVEs) in both cases where microstructure geometry information is complete and incomplete.