Volume Contents

As is known of glass fiber-reinforced plastics, the mechanical and physical properties of composites, next to the fiber properties, and the quality of the fiber matrix interface, as well as the textile form of the reinforcement primarily depend on the volume content of fibers in the composite. 

Tests by Roe et al. [63] with unidirectional jute fiber-reinforced UP resins show a linear relationship (analogous to the linear mixing rule) between the volume content of fiber and Young s modulus and tensile strength of the composite over a range of fiber content of 0-60%. Similar results are attained for the work of fracture and for the interlaminate shear strength (Fig. 20). Chawla et al. [64] found similar results for the flexural properties of jute fiber-UP composites. 

Table 1. The values of the characteristic parameters of a series of iron-epoxy particulates for various filler volume contents of... 

Fig. 6. The variation of the heat capacity jumps at the respective glass transition temperatures versus inclusion-volume contents of iron-epoxy particulates of different diameters of inclusions. In the same figure is presented the variation of the coefficients X for the same composites and volume contents...

As soon as the Ar s were determined and the values of r s are found, the values of the adhesion coefficient A may be readily defined by using relation (27). The values of A s for the different inclusion-volume contents studied are given in Table I for iron-epoxy particulate composites with different amounts of fillers, up to 25 percent l4>. 

Moreover, the mesophase-volume fractions Oj for the same inclusion-contents were determined from the experimental values of heat-capacity jumps ACp at the respective glass transition temperatures T f by applying Lipatov s theory. Fig. 7 presents the variation of the differences Ars oi the radii of the mesophase and the inclusion (rf), versus the inclusion volume content, uf, for three different diameters of inclusions varying between df = 150 pm and df = 400 pm. 

Fig. 7. The variation of the differences Ar, of the radii mesophases and inclusions (rf), versus the inclusion volume content uf for three different diameters of inclusions...

Fig. 8. The variation of the mesophase (i)j), and matrix, (vj, volume contents, versus the respective inclusion volume content, uf, for the three types of iron-epoxy particulates of respective diameters df = 150, 300 and 400 pm...

From the values of Ap for the various inclusion contents, the u, s and um s were calculated and plotted in Fig. 8, versus the inclusion volume content. It is apparent from these graphs that the mesophase volume content Uj for the three different diameters of inclusions varied only insignificantly and therefore they may be assumed as independent of the diameters of inclusions. 

Fig. 10. The variation of the mesophase moduli Ej(r) for the various filler volume contents of iron-epoxy particulates, versus the polar distance from the filler-matrix boundary...

It is interesting to point out the small variation of the average value of the variable Ef(r)-modulus of the mesophase, which reflects the uniformity of the adhesion quality of these series of composites, which is also indicated by the almost linear variation of the composite modulus, versus the volume content. 

In this relation the only unknown is the exponent 2q, which may be calculated by introducing the appropriate values for all known quantities, corresponding to each inclusion volume content of the particulate studied. 

The definition of the extent of mesophase and the evaluation of its radius r, is again based on the thermodynamic principle, introduced by Lipatov 11), and on measurements of the heat-capacity jumps AC and ACf, of the matrix material (AC ) and the fiber-composites (ACP) with different fiber-volume contents. These jumps appear at the glass-transition temperatures Tgc of the composites and they are intimately related, as it has been explained with particulates, to the volume fraction of the mesophase. 

Fig. 14. The variation of the specific heat jumps at glass-transition temperatures of elacc-epoxy composites, versus the fiber volume content, uf. The values for the factor X and the mesophase, (uj and matrix, (nm) volume fractions, versus uf, as derived from the values of the respective AC, s are also plotted...

From Ref. 22) the values of the composite moduli in the direction of the fibers were taken for various fiber-volume contents, whereas the mesophase volume fractions Uj were determined from the experimental values of these quantities for certain values of uf s, by applying the approximate multilayer model introduced by Ref. 4). These values fitted excellently a second degree curve expressed by ... 

Fig. 15. The variation of the adhesion coefficient A = (ri, — t 2) for the three-term unfolding model and the exponent 2r for the two-term model of a series of E-glass-epoxy fiber composites, versus the fiber-volume content uf...

Again, in this relation the only unknown is the exponent 2q. Then, by solving this equation the value of r can be derived for each fiber-volume content. The values of the exponent 2q were plotted in Fig. 15 and included in the Table 2. If one plots the variation of Ej(r), expressed by the three terms of the three-term unfolding model for a particular fiber-volume content, say for uf = 0.65, as it has been done in Fig. 17, and tries also to plot the same variation for E(r), as it is expressed by the two-term model, it may found that, although the contributing terms are different for each case, the derived values for the E.(r)-modulus are identical. This indicates that the two-term model is preferable, as simpler, since both models yield identical results, as they should give. 

Figure 3.47 Dependence of the volume contents of methane, hydrogen cyanide, carbon monoxide and carbon dioxide, normalized to the methane content, on the reaction temperature (measurements made by BASF) [2j.

The carbon dioxide volume content was varied from 0.8 to 100 vol.-% the gas velocity changes from 0.1 to 42.9 mm s [5]. The residence time varied from 0.1 to 9.7 min 64 single streams of a liquid film thickness of 65 pm were used at a total volume flow of 50 ml h . The ratio of carbon dioxide to sodium hydroxide was fixed at 0.4. 

GL 22] [R 1] [P 23] The mass transfer efficiency of the falling film micro reactor as a function of the carbon dioxide volume content was compared quantitatively (Figure 5.30) [5]. The molar ratio of carbon dioxide to sodium hydroxide was constant at 0.4 for all experiments, i.e. the liquid reactant was in slight excess. 

FIGURE 2.7 Change of electrical conductivity at 1000°C with respect to Ni volume content for Ni-YSZ cermets sintered for 2 h at 1200, 1250, 1300, and 1350°C, respectively. (From Pratihar, S.K. et al., Proceedings of the Sixth International Symposium on Solid Oxide Fuel Cells, 99(19) 513—521. Reproduced by permission of ECS-The Electrochemical Society.)... 

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