Stereology, the science of estimating three-dimensional quantities from two-dimensionally acquired measurements, has historically been the sole technique for microstructural quantification. Over the last decade, 3D characterization has begun to replace stereology with direct 3D quantification. While direct 3D quantification offers several advantages over stereology such as the absence of sectioning variation and superior quantification of complex shapes, it is not without its limitations.
Many in the 3D materials science community recognize the limited statistical confidence in most reconstructed volumes. Therefore, one objective of this work involved the use statistical tools such as random sampling and bootstrapping to establish quantitative relationships between sampled volume size and measurement precision for a variety of metrics across several microstructures. These quantitative relationships offered a unique opportunity. By determining analogous relationships between the precisions of two-dimensionally acquired metrics versus the amount of sampled area, a comparison between the representative area element (RAE) and representative volume element (RVE) has be made for a given precision. Such a comparison has served to advance the understanding of the influence of sectioning variation on stereological precision. Quantified relationships for several titanium microstructures will be presented along with a methodology to determine such relationships in other microstructures.
In addition to exploring the influence of sectioning variation on various stereological metrics, 3D characterization can serve to either validate or invalidate stereological assumptions. A common stereological metric is the mean linear intercept. Measured from a series of random lines placed within a segmented microstructure, the mean linear intercept has been employed to estimate three-dimensional quantities such as the mean diameter of spheroidal precipitates and mean width of plate-like features. In both cases, the constitutive equations rely of several assumptions regarding the shape and size distribution of the intercepted features. For features such as equiaxed-a and a-laths in a+ß titanium alloys, this thesis will explore the validity of these assumptions and determined the sensitivity of stereological quantification to deviations from such assumptions.
Three-dimensional materials characterization has undoubtedly advanced the understanding of numerous materials science phenomena and revealed the complexity of various microstructural features. The increasing number of applications of 3D characterization has established a series of processing procedures, the majority of which involve post-acquisition processing and analysis. As data acquisition techniques continue to advance and emerge, the need for more robust, materials science focused, analytical 3D software has become evident. This has led to the development of an all-inclusive, user-friendly software package known as MIPAR™ (Materials Image Processing and Automated Reconstruction). MIPAR™ was written and developed within the MATLAB™ environment, but is deployable as a standalone cross-platform application. MIPAR™ is structured around a modular layout. With a total of five modules, MIPAR™ was designed to handle all post-acquisition stages of 3D characterization: alignment, pre-processing, segmentation, visualization, and quantification. Its development has both driven the implementation of several 2D/3D filtering, segmentation, and quantification tools, and yielded a framework which can easily absorb additional processing techniques and serve as a launching platform for efficient algorithm development, implementation, and deployment.
In this work, MIPAR™, and the developed algorithms which it contains, have been applied for the 2D and 3D characterization of various titanium alloys. In the area of 3D characterization, results of MIPAR’s application have included validation of long-standing stereological relationships, the emergence of an assumption-free metric for estimating plate-like feature thickness, and the successful segmentation of challenging microstructural features known as a-colonies. With regard to 2D characterization, MIPAR™ has proven an effective platform for rapid microstructural characterization, where the results have been correlated with local mechanical properties and revealed a strong relationship between a-lath thickness and the degree of local strain. Furthermore, an advanced algorithm has been developed and applied for the segmentation of different phases from atomic-resolution electron micrographs and has also permitted a quantification of their structural interface width.
This thesis was able to accomplish many of its objectives and in some cases close areas of formerly open research. However, many areas still offer exciting opportunities for future work. The subjects of such work will be discussed in detail throughout the subsequent chapters.