Investigating the Relationships Between Material Properties and Microstructural Shapes as Quantified by Moment Invariants

The analysis of microstructural shapes is an underutilized tool in the field of materials science. Typical observations of morphology are qualitative, rather than quantitative, which prevents the identification of relationships between shape and the mechanical properties of a material. Recent advances in the fields of computer vision and high-dimensional analysis have made computer-based shape characterization feasible on a variety of materials. In this work, the relationship between microstructural shapes, and the properties and function of the material as a whole, is explored using moment invariants as global shape descriptors. A diifferent relationship is examined in each of three material systems: how the three-dimensional shapes of cells in the cotyledons of the plant Arabidopsis Thaliana can be used to identify cell function; the two-dimensional shapes of additive manufacturing feedstock powder and the ability to distinguish between images of powders from different samples; and the two-dimensional shapes of ' precipitates and their influence on the creep resistance of single crystal nickel-base superalloys. In the case of Arabidopsis Thaliana cotyledon cells, three-dimensional Zernike and Cartesian moment invariants were used to quantify morphology, and combined with size and orientation information. These feature sets were then analyzed using unsupervised and supervised machine learning methods. Moderate success was found using unsupervised methods, indicating that natural delineations in the data correlate to cell roles to some degree. Using supervised methods, a success rate of 90% was possible, indicating that these features can be used to identify cell function. The ability of two-dimensional Cartesian moment invariants to distinguish meaningful features in particles of additive manufacturing feedstock was tested by using these features to classify images of feedstock. Ultimately, simple histogram matching methods were unsuccessful, likely because they rely on the most common particles to draw conclusions. A bag-of-words method was used, which uses high-dimensional visualization and clustering techniques to classify individual particles by common features. Histograms of particle clusters are then used to represent each image. This method was far more successful, and a correct classification rate of up to 90% was found, and comparable rates were discovered using invariants which describe the shapes only broadly. This indicates that moment invariants are an effective measure of the morphologies of these types of particles, and can be used to classify powder shapes, which control many properties which are relevant to the additive manufacturing process. In the case of the superalloys, it has been shown that the shape distribution of ' precipitates can be tracked using second order moment invariants. In addition, several loworder moment invariants are shown to correlate to creep resistance in four alloys examined, which supports the idea that the shape of precipitates plays role in determining creep resistance in these alloys.