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We present a methodology for characterizing and reconstructing in-plane weave variability in textile composites. Surface topography of a partially processed C-fiber/SiC matrix composite panel was measured using digital image correlation. The centroids of tow segments that appear periodically on the fabric surface were located by image analysis and used as fiducial markers. Stochastic deviations of the fiducial markers from the ideal periodic weave structure indicate geometrical variance. Fourier analysis shows that spatial wavelengths of the deviations range from the size of one unit cell to the dimensions of the entire panel. Long-range deviations are attributed principally to fabric deformation after manufacture, during handling. Short-range fluctuations, extracted by computing spatial derivatives of the positions of the fiducial markers, are attributed to variations in tow packing density that arises during weaving. A simple set of statistics for these deviations is presented and its use in generating stochastic virtual specimens is demonstrated.

We review the development of virtual tests for high-temperature ceramic matrix composites with textile reinforcement. Success hinges on understanding the relationship between the microstructure of continuous-fiber composites, including its stochastic variability, and the evolution of damage events leading to failure. The virtual tests combine advanced experiments and theories to address physical, mathematical, and engineering aspects of material definition and failure prediction. Key new experiments include surface image correlation methods and synchrotron-based, micrometer-resolution 3D imaging, both executed at temperatures exceeding 1,500• C. Computational methods include new probabilistic algorithms for generating stochastic virtual specimens, as well as a new augmented finite element method that deals efficiently with arbitrary systems of crack initiation, bifurcation, and coalescence in heterogeneous materials. Conceptual advances include the use of topology to characterize stochastic microstructures. We discuss the challenge of predicting the probability of an extreme failure event in a computationally tractable manner while retaining the necessary physical detail. 17.1

This paper presents a generalized framework along with the associated computational strategies for a rigorous quantification of the material structure in a range of different applications using the framework of 2-point spatial correlations. In particular, we focus on applications requiring different assumptions about the periodicity and/or involving irregular domain shapes and potentially extremely large datasets. Important details of the computational algorithms needed to address these challenges are developed and illustrated with example case studies. Algorithms developed and presented in this work are available at http://dx.doi.org/10.5281/zenodo.31329. Background