Three-cylinder composite model

Fig. 4.31. Distributions of (a) fiber axial stress and (b) interface shear stress along the axial direction obtained from micromechanics analysis for different fiber volume fractions, Vf = 0.03, 0.3 and 0.6 (—) single fiber composite (--------) three cylinder composite model. After Kim et al. (1994b).

In the light of the discussion presented in Section 4.3.6, it is seen that the surrounding composite medium in the three-cylinder composite model acts as a stiff annulus to suppress the development of IFSS at the embedded fiber end by constraining the radial boundary of the matrix cylinder. This ensures that regardless... 

Fig. 7.13. Schematic drawing of a three-cylinder composite model with an infinite matrix radius. After...

Fig, 4.30. Schematic illustrations of the finite clement models of (a) single fiber pull-out specimen and (b) a three cylinder composite. After Kim ct al. (1994b). 

For analytical purposes, the fiber composites are conveniently modeled using axisymmetric three-phase (i.e. fiber-interlayer-matrix), four-phase (i.e. fiber-interlayer-matrix-composite medium) cylindrical composites, or in rare cases multi-layer composites (Zhang, 1993). These models are schematically presented in Fig. 7.9. The three-phase uniform interphase model is typified by the work of Nairn (1985) and Beneveniste et al. (1989), while Mitaka and Taya (1985a, b, 1986) were the pioneers in developing four-phase models with interlayer/interphase of varying stiffness and CTE values to characterize the stress fields due to thermo-mechanical loading. The four phase composite models contain another cylinder at the outermost surface as an equivalent composite (Christensen, 1979 Theocaris and Demakos, 1992 Lhotellier and Brinson, 1988). 

Fig. 4. Previous (A) and updated (B) model of the phycobilisome of Mastigocladus laminosus showing the location and polypeptide composition (phycobiliproteins, linker polypeptides) of the complexes making up the r s and the three-cylinder core. (1) Lr -, ...

A three-layer model for fiber composites may be developed, based on the theory of self-consistent models and adapting this theory to a three-layered cylinder, delineating the representative volume element for the fiber composite. 

A better approach for the Rosen-Hashin models is to adopt models, whose representative volume element consists of three phases, which are either concentric spheres for the particulates, or co-axial cylinders for the fiber-composites, with each phase maintaining its constant volume fraction 4). 

In this paper, we now report measurements of heat transfer coefficients for three systems at a variety of compositions near their lower consolute points. The first two, n-pentane--CO2 and n-decane--C02 are supercritical. The third is a liquid--liquid mixture, triethylamine (TEA)--H20, at atmospheric pressure. It seems to be quite analogous and exhibits similar behavior. All measurements were made using an electrically heated, horizontal copper cylinder in free convection. An attempt to interpret the results is given based on a scale analysis. This leads us to the conclusion that no attempt at modeling the observed condensation behavior will be possible without taking into account the possibility of interfacial tension-driven flows. However, other factors, which have so far eluded definition, appear to be involved. 

The composite could be simplified in term of a three dimensional array of identical hexagonal cylindrical cells, and the carbide reinforcements are located in the center of each cell (Figure 3), which can be further approximated to a periodic array of cylinders. Only one half of the cylindrical cell needs to be analyzed. The finite element model is shown in Figure 4, the boundaries of ODE and OBC remain stationary because these are lines of symmetry in the cylinder, and the lines EF and FC remain parallel to their original directions arising from the equal and the opposite forces of neighbor cells at these boundaries. 8-node quadrilateral axisymmetric element is used for the calculation. 

---