Modeling Anisotropic Multiphase Heterogeneous Materials via Directional Correlation Functions: Simulations and Experimen
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Heterogeneous materials, such as composites materials or metallic alloys, are ubiquitous. In composites, the effective properties are determined by their complex microstructures (e.g., the volume fraction, morphology, and spatial distribution of different phases).[1,2] Aluminum alloys and steel almost always have second phase inclusions and particles with impurities that are present in the microstructure. A quantitative understanding of the structure–property relationship in such materials has begun to emerge over the past few decades, mainly because of the development of advanced experimental and computational materials microstructure characterization techniques.[3] In particular, X-ray tomography techniques have been widely used to obtain high-resolution three-dimensional (3D) microstructure for a wide range of heterogeneous materials. X-ray tomography is an excellent
SUDHANSHU S. SINGH, Graduate Research Assistant, JASON J. WILLIAMS, Research Scientist, and NIKHILESH CHAWLA, Fulton Professor, are with the Materials Science and Engineering, Arizona State University, Tempe, AZ 85287-6206. Contact e-mail: [email protected] YANG JIAO, Postdoctoral Fellow, formerly with the Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, NJ 08540, is now Assistant Professor with Materials Science and Engineering, Arizona State University. Manuscript submitted: July 9, 2012. METALLURGICAL AND MATERIALS TRANSACTIONS A
technique that eliminates destructive cross-sectioning, and allows for superior resolution and image quality with minimal sample preparation.[4,5] 3D visualization and quantification of heterogeneous microstructures by X-ray tomography have been successfully performed in Sn-rich alloys,[6] powder metallurgy steels,[7] metal matrix composites,[8–12] and lightweight alloys.[13–17] In addition to visualization, such microstructural datasets can be incorporated into finite element models to predict the onset of local damage mechanisms and the macroscopic deformation behavior.[18–22] One of the most time-consuming parts of the 3D X-ray tomography process is segmentation of gray-scale images and 3D reconstruction of the segmented image dataset. Such a 3D dataset is a prerequisite for quantification of salient microstructural features.[11,23] A simpler and more efficient method for developing realistic 3D microstructures, which are statistically and visually descriptive of the actual microstructure of the material, is required. Recently, it has been suggested that the complex microstructures of a wide class of heterogeneous materials can be modeled by certain statistical morphologic descriptors associated with the materials, i.e., lowerorder spatial correlation functions of the material phases.[24,25] Efficient microstructure’s reconstruction procedures incorporating such correlation functions have been developed, which enable one to ascertain the amount of structural information contained in these statistical descriptors.[26–32] Specifically, the standard two-point correlation func
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