The Fiber Phase

Reinforcement Efficiency of Fiber-Reinforced Composites for Several Fiber Orientations and at Various Directions of Stress Application 

Fiber Orientation Stress Direction Reinforcement Efficiency 

Fibers randomly and uniformly distributed within three dimensions in space Any direction 1 5 

Source H. Krenchel, Fibre Reinforcement, Copenhagen Akademisk Forlag, 1964 [33]. 

By way of summary, then, we say that aligned fibrous composites are inherently anisotropic in that the maximum strength and reinforcement are achieved along the aUgmnent (longitudinal) direction. In the transverse direction, fiber reinforcement is virtually nonexistent fracture usually occurs at relatively low tensile stresses. For other stress orientations, composite strength lies between these extremes. The efficiency of fiber reinforcement for several situations is presented in Table 16.3 this efficiency is taken to be unity for an oriented-fiber composite in the alignment direction and zero perpendicular to it. 

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In the dyeing process absorption from the dyebath solution to the fiber eventually stops when an equiHbrium exists between the dye in the fiber phase and the dye in the solution phase. At this point by definition (no movement of dye molecules), therefore... 

Influence of the Fiber. In order for a dye to move from the aqueous dyebath to the fiber phase the combination of dye and fiber must be at a lower energy level than dye and water. This in turn implies that there is a more efficient, lower energy sharing of electrons or intramolecular energy forces, and there are a number of mechanisms that allow this to happen. 

We have chosen to call the two phases resin and fiber. Each phase will be denoted by subscript r and respectively. A similar phase function (i.e., Yf) can be defined for the fiber phase. It should be noted that if the fiber phase is stationary Y is not a function of time. 

As mentioned earlier, the expression forfd is obtained under conditions of no inertia. If we further assume the resin is Newtonian (i.e., r = p[V Ur + V / ])) and the fiber phase is stationary, then Equation 5.25 can be simplified to the well-known Brinkman equation [22],... 

Since the fiber phase is not stationary, the surface integral cannot be set to zero without further considerations. As shown earlier, dBr/dt = 1/V js Ur hids (see Eq. 5.10). Because der/dt = 0 in the IP process, the contribution of the surface integral to the overall mass balance is negligible. Based on this observation Equation 5.50 can be simplified mid the appropriate equation for a conservation of mass in this process can be obtained (i.e., V Ur) = 0). Using this, Equation 5.18 can be simplified and the appropriate species balance equation for the IP process can be obtained. This equation is similar to the equation obtained for the RTM process. 

The movement of the fiber phase has to be specifically taken into consideration in the momentum transfer equation. Hence, in absence of significant inertial forces (i.e., Rep < l)3 Equation 5.28 must be modified to account for the movement of the fiber phase,... 

The practical characteristic of a dyestuff is that when a textile is immersed in a solution containing a dye. the dye preferentially adsorbs onto and diffuses into the texiile. The thermodynamic equations defining this process have been reviewed in detail. The driving force for this adsorption process is the difference in chemical potential between the dye In the solution phase and the dye in the fiber phase. In practice it is only necessary to consider changes in chemical potential and to understand that the driving force is the reduction in free energy associated with the dye molecule moving from one phase to the other, as the molecule always moves to the siate of lowest chemical potential. 

Gas chromatography/olfactometry (GC/O) based on dilution analysis (e.g., CharmAna-lysis or Aroma Extraction Dilution Analysis) gives an indication of what compounds are most potent in the aroma of foods. The application of SPME to GC/O dilution analysis can be achieved by varying the thickness of the fiber phase and the length of exposure, resulting in various absorbant volumes. 

As expected, the matrix deviatoric stresses will be relaxed away completely. Thereafter, the fiber phase sustains the entire deviatoric stress. As a consequence, in the asymptotic state... 

In the early 90s, a new technique called solid-phase-micro extraction (SPME), was developed (Arthur and Pawliszyn, 1990). The key-part component of the SPME device is a fused silica fiber coated with an adsorbent material such as polydimethylsiloxane (PDMS), polyacrylate (PA) and carbowax (CW), or mixed phases such as polydimethylsiloxane-divinylbenzene (PDMS-DVB), carboxen-polydimethylsiloxane (CAR-PDMS) and carboxen-polydimethyl-siloxane-divinylbenzene (CAR-PDMS-DVB). The sampling can be made either in the headspace (Vas et al., 1998) or in the liquid phase (De la Calle et al., 1996) of the samples. The headspace sampling in wine analyses is mainly useful for quantifying trace compounds with a particular affinity to the fiber phase, not easily measurable with other techniques. Exhaustive overviews on materials used for the extraction-concentration of aroma compounds were published by Ferreira et al. (1996), Eberler (2001), Cabredo-Pinillos et al. (2004) and Nongonierma et al. (2006). Analysis of the volatile compounds is usually performed by gas chromatography (GC) coupled with either a flame ionization (FID) or mass spectrometry (MS) detector. 

Headspace is useful for the trace analysis of compounds having a high affinity for the fiber phase and that can be enriched in the HS of the sample. The use of a multiphase fiber is a very interesting and low time-consuming approach. It also considers the possibility of sampling automation using a GC/MS system coupled with a statistical method for treatment of fragment abundance (Kinton et al., 2003 Cozzolino et al.,2006). 

Fig. 5. Sample plot showing the MOR values for some of the batches extmded into rods, and fired at three different temperatures, 300, 600 1000°C, for 3hrs. MOR values increase with firing temperature, which may be due to the onset of sintering. This hypothesis is corroborated by the reduction in specific surface area observed. For comparison, MOR value for fired Cordierite rods, of comparable porosity, is shown by the dashed line. The five batches shown here differ in compositional details like the particle size distribution (PSD) of the filler phase used and the amount of the fiber phase, colloidal sihca phase used.

Hill (1963) suggested that there is a unique dependence of the fiber-phase average strain, on the overall average strain of the composite, sy, given as... 

The theory of SPME can be extended from the classical liquid-liquid extraction theory described above (61). Since in most SPME analyses, analytes are volatile and dissolved in an aqueous phase, a three-phase system, including the aqueous phase, the fiber phase, and the headspace phase above the aqueous, is described. The mass of analyte extracted into the fiber phase is given by... 

Succeeding to the above analysis, the question for the sequence of substitutions arises again in consideration of two appropriate possibilities. In accordance with Remark 5.6, either the results of the stacking in the transverse directions. Section 5.4.4, are utilized to represent the fiber phase for the stacking in the fiber direction. Section 5.4.5, or the other way round. These possibilities are illustrated in Figures 5.10(a) and (b), respectively, and may be written S3Tnbolically as... 

Polymer matrices generally are relatively weak, low-stiffness, viscoelastic materials. They also have very low thermal and electrical conductivities. The strength and stiffness of PMCs come primarily from the fiber phase. 

Let us now consider the elastic behavior of a continuous and oriented fibrous composite that is loaded in the direction of fiber ahgnment. First, it is assumed that the fiber-matrix interfacial bond is very good, such that deformation of both matrix and fibers is the same (an isostrain situation). Under these conditions, the total load sustained by the composite is equal to the sum of the loads carried by the matrix phase and the fiber phase Ff, or... 

Thus, the fiber phase supports the vast majority of the applied load. 

The Fiber Phase On the basis of diameter and material type, fiber reinforcements are classified as follows Whiskers —extremely strong single crystals that have very small diameters Fibers —normally polymers or ceramics that may be either amorphous or polycrystalline... 

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