The objectives of this research program are: (1) to develop new quantitative fractographic, stereological, and digital image analysis techniques for characterization of microstructures and fracture surfaces: (2) to develop image analysis and microstructure modeling techniques to incorporate detailed quantitative microstructural information in the finite elements-based simulations of mechanical response of complex microstructures; and (3) to apply the new techniques in the study of deformation, damage evolution, and fracture behavior of materials. The analytical theoretical work involves applications of stochastic geometry and global analysis. New stereological and quantitative fractographic relationships are derived for efficient, unbiased estimation of geometric attributes of microstructures and fracture surfaces in three-dimensional space from measurements performed on lower dimensional manifolds such as two dimensional sections and projections. Under development are digital image analysis techniques to link microstructural length scales for finite elements-based simulations of deformation and fracture. Image analysis techniques are used to create large area high resolution "montages" of fractographic SEM images and stereo-pair images to quantify spatial arrangement of features (for example, voids, inclusions, etc.) on fracture surfaces. Experimental work on monolithic and composite materials involves stereological and fractographic measurements that demonstrate the applications of the techniques developed in the above tasks. %%% The study of microstructures is central to materials science and numerous other disciplines where microscopy is used to characterize internal structure. Apart from materials science, the results of this research are also relevant and useful in a variety of different disciplines such as anatomy, neuro-science, cell biology, plant physiology, stochastic geometry, and global analysis. ***
