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Rheology of highly concentrated planar fiber suspensions
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View: Figures


Image of FIG. 1.
FIG. 1.

Homogenization method for discrete and periodic media: basic principle and specific asymptotic expansions.

Image of FIG. 2.
FIG. 2.

Optical micrographies showing typical glass fiber-bundles used in industrial SMC: (a) top view of bundles, (b) cross-sections of bundles, (c) idealization of bundles geometry.

Image of FIG. 3.
FIG. 3.

Modeling of bundle-bundle local interactions: side view of the interaction zone (b), top view of the interaction surface approximation for local moments evaluation (c).

Image of FIG. 4.
FIG. 4.

Example of generated representative elementary volume , containing 437 bundles of length 25 mm . Open circles represent the connections location, lines represent the centerline of the bundles .

Image of FIG. 5.
FIG. 5.

Approximation of the orientation distribution function given by the second-order orientation tensor in the case of a quasi-isotropic microstructure (, , ) (a), and of an oriented microstructure (, , ) (b).

Image of FIG. 6.
FIG. 6.

Evolution of the relative orientation functions and with the major eigenvalue of the second order orientation tensor .

Image of FIG. 7.
FIG. 7.

Typical experimental response of SMC of fiber content (Dumont et al., 2003): simple compression test (a) and a plane strain compression test (b), both performed at an axial strain rate -Comparison with the results of the micro-macro model.

Image of FIG. 8.
FIG. 8.

Admissible range of values of parameters and determined from a unique simple compression test (Dumont et al., 2003; Le Corre et al., 2002).

Image of FIG. 9.
FIG. 9.

Evolution of the normalized threshold viscosities with the volume fraction of bundles, comparison with experimental results obtained on an industrial SMC (Dumont et al., 2003): (a) axial component in simple compression (33sc), (b) axial component in plane strain compression (33ps), (c) lateral component in plane strain compression (22ps).

Image of FIG. 10.
FIG. 10.

Influence of the axial strain-rate on the threshold stresses for a random suspension with various bundle content, comparison with experimental results of Dumont et al. (2003).

Image of FIG. 11.
FIG. 11.

Influence of the orientation intensity , for fiber networks undergoing a plane strain deformation along , , and for : (a) components of , (b) components of .

Image of FIG. 12.
FIG. 12.

Evolution of the fraction , where is the number of bundles such as and abscissa is a condition expressed in %—different bundle networks with and , submitted to four macroscopic strain rates: plane strain along , plane strain along , pure shear in direction 12, simple compression-(a) random orientation (, ), (b) rather oriented (, ), (c) very oriented (, ).


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Rheology of highly concentrated planar fiber suspensions