Materials—(a) Evolution of the steady state shear viscosity μ of the suspending fluid with the shear strain rate at 50 °C (dots represent the experimental data and the continuous line the Carreau fit). (b) 3D view and cross section of a glass fiber bundle (x-ray microtomography, voxel size ).
3D micrographs obtained from a fiber bundle suspension with . (a) 3D map of the x-ray absorption coefficient (voxel size 15.6 μm); (b) 3D overview of the fibrous network after thresholding; (c) and (g) 3D views showing the continuous fiber bundle (green) and the short fiber bundles (red) in contact with it; (d)–(f): zooms on a bundle–bundle contact with a 3D view (d), an upper view (e) and a cross section along one of the two fiber bundles (f) (voxel size 3.2 μm).
Scheme of the pull-out apparatus.
Method used to estimate fibrous microstructure descriptors. From the segmented volume (a), the bundle centerlines are determined (b), then the bundle network is numerically generated (c) so that the bundle–bundle contacts can be detected (d).
Orientation of the bundles (a) and of the bundle–bundle contacts (c) in the volume (b).
Stress–strain (a) and stress-time (b) curves recorded during two lubricated simple compressions performed using a suspension with at a constant compression strain rate of 0.1 s−1 and with two different final compression strains.
Evolution of the consolidation stress with respect to the fiber content at a consolidation strain rate of 0.1 s−1. The two sets of data have been obtained with a dry fibrous mat and with the bundle suspension heated at 120°. The continuous lines represent the fit given by expression (8).
Typical evolution of the drag force with respect to the pull-out length recorded for the suspending fluid (a) and for the suspension (b). In graph (a), the five experimental curves are obtained by extracting successively the five continuous bundles. In graph (b), they are obtained for different samples and different initial conditions.
Evolution of the pull-out force in various testing conditions. (a): curves showing the influence of the confining stress . (b) Same tests but with graph. (c) and (d): curves showing the influence of the pull-out velocity and the fiber content φ, respectively.
Evolution of the drag coefficient with the confining stress (a), the pull-out velocity (b) and the fiber content φ (c). Continuous lines are the predictions given by the proposed pull-out model.
Method used to estimate for φ = 0.13. (a) and (b) Along the continuous bundle, orthogonal slices were extracted from 3D micrographs. (c) and (d) Slice idealization used to run the FEM calculations. In the case where slices are located in a bundle–bundle contact zone (d), only the half space was modeled and a symmetry condition was set on . Color maps given in (c) and (d) represent the norm of the velocity field ranging linearly from zero (blue) to (red). (e) Evolution of the computed drag coefficient with (marks) and fits of Eq. (15) used to capture numerical results (continuous lines).
Evolution of the drag coefficient with for the suspending fluid (a). The continuous line shown in this graph is the best fit obtained by an inverse modeling that used a direct FE calculation: a zoom of the corresponding P2-P1 mesh around the cross section of the extracted bundle is shown in (b).
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