Topological and Euclidean metrics reveal spatially nonuniform structure in the entanglement of stochastic fiber bundles

Data acquired from synchrotron-based X-ray computed tomography provide complete descriptions of the stochastic positions of each fiber in large bundles within composite samples. The data can be accumulated for distances along the nominal fiber direction that are long enough to reveal meandering or misalignment. Data are analyzed for a single fiber bundle consolidated as a mini-composite specimen and a block of fibers embedded within a single ply in a tape laminate specimen. The fibers in these materials differ markedly in their departure from alignment and the patterns formed by fiber deviations. The tape laminate specimen exhibits evidence of fibers that have slipped laterally through the bundle in narrow shear bands, which may be a mechanism of bundle deformation under transverse compression and shear. This pattern is absent in the single-tow specimen, which was not subject to transverse loads in processing. We propose a combination of topological and Euclidean metrics to quantify these and other stochastic bundle characteristics. Topological metrics are based on the neighbor map of fibers, which is constructed on cross-sections of the bundle by Delaunay triangulation (or Voronoi tessellation). Variations of the neighbor map along the fiber direction describe fiber meandering, twist, etc. Euclidean metrics include factors such as local fiber density and fiber orientation. The metrics distinguish bundle types, enable quantification of the effects of the manufacturing history of bundles, and provide target statistics to be matched by virtual specimens that might be generated for use in fiber-scale virtual tests.