Computational Physics Group

Karel Matous










Microstructure Statistics Property Relations of Anisotropic
Polydisperse Particulate Composites using Tomography

A. Gillman, K. Matous and S. Atkinson

Department of Aerospace and Mechanical Engineering
University of Notre Dame
Notre Dame, IN, 46556, USA.


    In this paper, a systematic method is presented for developing microstructure-statistics-property relations of anisotropic polydisperse particulate composites using micro-computer tomography (micro-CT). Micro-CT is used to obtain a detailed three-dimensional representation of polydisperse microstructures, and a novel image processing pipeline is developed for identifying particles. In this work, particles are modeled as idealized shapes in order to guide the image processing steps and to provide a description of the discrete micro-CT dataset in continuous Euclidean space. n-point probability functions used to describe the morphology of mixtures are calculated directly from real microstructures. The statistical descriptors are employed in the Hashin-Shtrikman variational principle to compute overall anisotropic bounds and self-consistent estimates of the thermal conductivity tensor. We make no assumptions of statistical isotropy nor ellipsoidal symmetry, and the statistical description is obtained directly from micro-CT data. Various mixtures consisting of polydisperse ellipsoidal and spherical particles are prepared and studied to show how the morphology impacts the overall anisotropic thermal conductivity tensor.


    In this work, we present a systematic microstructure characterization procedure anchored in micro-CT data that is used to establish microstructure-statistics-property relations of polydisperse particulate mixtures. A novel image processing pipeline is developed that accurately identifies particles while maintaining low errors. Improvements in the image processing pipeline are achieved when compared to a traditional technique. For all compositions considered, the volume losses due to image segmentation are less than 4%. These low errors indicate that scientifically sound and repeatable results have been achieved. Next, we developed a description of the polydisperse system in continuous Euclidean space. This idealized representation provides a substantial reduction in the dataset size and enables easier data manipulation and understanding.
    After characterizing the microstructure, three-dimensional n-point probability functions of real polydisperse mixtures are calculated. We show that second-order probability functions do not exhibit ellipsoidal nor any other material symmetry. Therefore, assessment of overall material constants in a closed form is unattainable.
    The statistical description is then used to compute bounds and self-consistent estimates of the anisotropic thermal conductivity tensor using the Hashin-Shtrikman variational principle. This is the first time to the best of our knowledge, that the anisotropic second-order estimates of polydisperse composites are calculated without assumptions on an inclusion’s shape, configuration and/or material anisotropy. The overall properties show increasing anisotropy in the overall thermal conductivity tensor for packs with more transverse isotropic ellipsoidal inclusions. Moreover, the upper and lower bounds provide limits on the anisotropy of the mixtures. Due to the larger amounts of statistical anisotropy for the semi-ordered mixture, the measure of anisotropy for the overall conductivity tensor of this pack was significantly larger than for the randomized one.


    The authors would like to acknowledge support from IllinoisRocstar LLC under the contract number FA9300-10-C-3003 (Edwards Air Force Base, SBIR Phase II project) by the Office of the Secretary of Defense as a part of the Phase II SBIR program.

    Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of IllinoisRocstar LLC and the U.S. Air Force.

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© 2013 Notre Dame and Dr. Karel Matous