A physical model, previously developed by one of the authors, has been extended to cover thermal conductivity degradation owing to the uni-axial stress-strain response of aligned groups of fibres or tows found in ceramic matrix composites. Both the stress-strain and thermal models, together with their coupling, have been shown to predict known composite behaviour qualitatively. The degradation of longitudinal thermal properties is shown to be driven by strain-controlled fibre failure; while the degradation of transverse thermal properties is because of the growth of fibre-matrix interface wake-debonded cracks, coupled with strain-driven fibre failure.

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Three‐dimensional (3‐D) images of two ceramic‐matrix textile composites were captured by X‐ray micron‐resolution computed tomography (μCT) on a synchrotron beamline. Compared to optical images of sections, CT data reveal comprehensive geometrical information about the fiber tows; information at smaller scales, on matrix voids, individual fibers, and fiber coatings, can also be extracted but image artifacts can compromise interpretation. A statistical analysis of the shape and positioning of the fiber tows in the 3‐D woven architecture is performed, based on a decomposition of the spatial variations of any geometrical characteristic of the tows into non‐stochastic periodic trends and non‐periodic stochastic deviations. The periodic trends are compiled by exploiting the nominal translational invariance of the textile, a process that maximizes the information content of the relatively small specimens that can be imaged at high resolution. The stochastic deviations (or geometrical defects in the textile) are summarized in terms of the standard deviation of any characteristic at a single point along the axis of a tow and correlations between the values of deviations at two different points on the same or different tows. The tow characteristics analyzed consist of the coordinates of the centroids of a tow, together with the area, aspect ratio, and orientation of its cross‐section. The tabulated statistics are sufficient to calibrate a probabilistic generator (detailed elsewhere) that can create virtual specimens of any size that are individually distinct but share the statistical characteristics of the small specimens analyzed by X‐ray μCT. The data analysis presented herein forms the first step in formulating a virtual test of textile composites, by providing the statistical information required for realistic description of the textile reinforcement.

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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