Characterizing In‐Plane Geometrical Variability in Textile Ceramic Composites

Abstract

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.

Stochastic Virtual Tests for High-Temperature Ceramic Matrix Composites

“…k ) of typically 100 mm for weft tows and 50 mm for warp tows (75). Interestingly, data obtained by similar experimental analysis of a 2D twill weave show very similar qualitative variations in tow packing density (76).…”

“…with k denoting one of N δ stochastic Fourier coefficients whose amplitudes follow a normal distribution with mean A k , RMSD σ k , and correlation length ζ (75). For the particular material of Figure 4, δ xx and δ yy reveal alternating bands of high and low relative packing density, with fluctuations of magnitude ∼1% for the weft tows (δ xx ) and ∼3% for the warp tows (δ yy ).…”

“…Shorter-wavelength variations are also present but have smaller amplitude, and their characterization therefore requires the long-wavelength deviations to be filtered out. This can be accomplished by forming spatial derivatives of the deviations (75). fluctuations in relative tow spacing or packing density of the warp tows; an analogous derivative δ xx = δu i /δx does the same for weft tows.…”

“…fluctuations in relative tow spacing or packing density of the warp tows; an analogous derivative δ xx = δu i /δx does the same for weft tows. The derivative δ xy = (δu i /δy + δv i /δx)/2 can also be computed and measures the angle between the warp and weft tows (75). A virtual specimen should incorporate deviations created during manufacture, because these are intrinsic to the material, while excluding deviations that are likely to have arisen due to handling, because these are the response of the material to loads and would therefore be predicted by simulations, rather than being built into the specimen being simulated.…”

“…Therefore, statistical analysis of the data in Figure 4 focuses on the deviations in tow packing density, δ xx and δ yy . Large-amplitude, long-wavelength trends in δ xx , δ yy , and δ xy are ignored because they are believed to be caused by handling (75); short-range variations in δ xy appear implicitly in the analysis of δ xx and δ yy (75).…”