13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- modeled by direct experimentation. In the case of virtual tests for continuous-fiber composites, including composites reinforced by laminated unidirectional fiber plies and textile preforms, the high resolution now available in 3D imaging systems is yielding details of the stochastic variability of plies and fiber tows and even of the spatial distribution of the individual fibers that populate the plies and tows; certain characteristics of textile geometry and tow deformation have been measured [7-9], as well as porosity [10] and its changes during processing steps [10, 11]. These and other studies have also addressed achieving feature definition in ceramic composites [12], which is often made difficult by low x-ray absorption contrast between the constituent materials. In recent work, fiber tows are made to stand out by imaging composites with partially formed matrices [13]. This allows detailed analysis of the statistics of geometrical variability in the fiber reinforcement. The geometrical variability of fiber deployment is a source of scatter in composite performance [14-19]. In the remainder of this article, the sequential steps of constructing a virtual test are described. Interesting prior literature includes virtual tests for textile ceramic composites using models that directly reproduce a stochastic microstructure from micrographs [20] (rather than using a virtual specimen generator as described below). 2. The stochastic characteristics of textile composites The details of fiber tow shape in textile composite specimens somewhat larger than but comparable in size to a single unit cell (several mm) can be determined most satisfactorily using micron-resolution X-ray computed tomography (μCT) in a high-flux synchrotron beamline. Avoiding the difficulty of reconstructing 3D domains from 2D images of serial sections in micro-toming techniques, μCT data reveal comprehensive geometrical information on the fiber tow scale. Information at even smaller scales, down to 1 μm, concerning matrix voids, individual fibers, and fiber coatings can also be extracted but image artefacts can compromise interpretation. Typical images of a 3D woven carbon/SiC composite are shown in Fig. 1. (This material was fabricated with only enough matrix to rigidify the structure, which simplified identifying tow domains [13].) (a) (b) Figure 1. μCT of a carbon/SiC woven composite, consisting of fiber tows coated by a thin layer of matrix material. (a) Image slices. (b) Re-constructed 3D image. Fiber positioning variations can be decomposed into non-stochastic, periodic variations associated with the nominal periodicity in the textile architecture and stochastic deviations, which vary randomly though the fabric. A convenient and intuitively appealing treatment of the deviation divides it in turn into a superposition of “short-range” and “long-range” deviations. The
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