Microstructural Quantification and Property Prediction Using Limited X-ray Tomography Data

Abstract

X-ray tomography has provided a non-destructive means for microstructure characterization in three dimensional (3D) and four dimensional (4D) (i.e., structural evolution over time), in which projections of a material’s structure are typically reconstructed using the filtered-back-projection (FBP) method or algebraic reconstruction techniques. The reconstructed images are typically segmented to conduct microstructural quantification. The process can be quite time consuming and computationally intensive. In this paper, we present an overview of our recent work on utilizing a limited (Nyquist under-sampled) number of unique perspective radiographs for computed tomography reconstruction of heterogeneous material (e.g., composites and alloys) structural quantification, property prediction and microstructural reconstruction in 3D and 4D. The proposed approach is significantly more efficient and computationally less intensive than FBP. We first show that an inverse superposition of properly normalized attenuated intensity along different x-ray paths leads to a probability map for the material system, which provides the probability of finding a particular phase at a point in the imaged sample volume. Spatial correlation functions, which are statistical morphological descriptors of the material, are readily computed from the associated probability map. Using effective medium theory and the computed correlation functions, accurate predictions of physical properties (e.g., elastic moduli and thermal/electrical conductivity) can then be obtained. Finally, we present a stochastic reconstruction procedure that generates an accurate rendition of the 3D microstructure from a reduced number of tomographic projections. This stochastic reconstruction method can be easily adapted to reconstruct 4D structural evolution from a small number of in situ projections.