Fibre aspect ratio

The mean fibre length determines the fibre aspect ratio. One theory considers the effects of inclusions, of a given aspect ratio, surrounded by a material with the average properties of the composite. Figure 4.29a shows predictions for E-glass inclusions ( = 73GPa, p = 0.22) in an epoxy matrix (E = 5.35 GPa, v = 0.34) there is a steady increase in the composite modulus Ell in the direction of the perfectly aligned inclusions, as the aspect ratio and the fibre volume fraction increase. 

Variation of longitudinal Young s modulus of glass-fibre-reinforced PP with (a) Fibre aspect ratio and volume fraction (Chao, L.-P. and Wang, Y.-S., Polym. Compos., 21,20 2000) John Wiley and Sons Inc. reprinted with permission (b) orientation average cos 6 (Mine, R H. et ai, Compos. Sci. Tech., 64, 1081,2004) Elsevier. Dashed line, constant strain solid line, constant stress averaging. 

Finally, by recalling that the fibre aspect ratio a is l/d, we obtain the solution for af. 

The major factors that govern the properties of short-fibre thermoplastic composites are fibre volume fraction, fibre dispersion, fibre aspect ratio and length distribution, fibre orientation and fibre-matrix adhesion. Each of these parameters is briefly discussed below. 

The fibre aspect ratio, which is its length to diameter ratio is a critical parameter in a composite. A relationship has been proposed by Cox to relate the critical fibre aspect ratio, IJd, to the interfacial shear stress, Zy, viz. ... 

The condition for maximum reinforcement, that is the condition ensuring maximum stress transfer to the fibres, before the composite fails, is to have a length higher than the critical length (Fig. 19.5). If the fibre aspect ratio is lower than its critical value, the fibres are not loaded to their maximum stress value. A specificity of cellulose fibres is their flexibility compared to glass fibres which allows a desirable fibre aspect ratio to be maintained after processing, which is around 100 or 200 for high performance short-fibre composites. 

Figure 19.5 Variation of tensile stress in fibre and shear stress at interface occurring along the fibre length. If the fibre aspect ratio is lower than its critical value, l, the fibres are not loaded to their maximum stress value.

Fibre-matrix adhesive strength is unimportant for the modulus of compounds, which is determined by the volume fraction of fibres, the moduli of fibres and matrix, the fibre aspect ratio and the fibre orientation. The modulus is a small-strain property and the matrix shrinkage is usually sufficiently high to ensure the modulus increase desired without any true adhesion [4]. 

The three most important aspects to be characterized in fibre reinforced compounds are fibre aspect ratio, 1/d, fibre orientation and fibre-matrix adhesion, (1/d). An experimental difficulty in studying the processing-structure-properties relationships in these materials is the strongly coupled interrelations of interfaces and processing on the microstructure. 

George et al. [27] studied stress relaxation behaviour of pineapple fibre-reinforced polyethylene composites. They found stress relaxation to be decreased with an increase of fibre content due to better reinforcing effect It is also reported by George et al. [28] that properties of fibre-reinforced composites depend on many factors like fibre-matrix adhesion, volume fraction of fibre, fibre aspect ratio, fibre orientation as well as stress transfer efficiency of the interface. Luo and Netravah [29] found an increase in the mechanical properties of green composites prepared from PALFs and poly(hydroxybutyrate-co-valerate) resin (a biodegradable polymer) with the fibres in the longitudinal direction. However, the researchers reported a negative effect of the fibres on the properties in the transverse direction. 

Figure 12.5 Influence of steel fibre volume fraction on the workability of cement-based materials for different fibre aspect ratios /d, after Edgington etal (1974).

In the first solution, the highest values of and have been for steel fibres of volume fraction V and fibre aspect ratio L/d. In the second problem, the optimization of cost, which means minimum volume of fibres was looked for. In both problems the importance of variables was the same, that is, all variables were considered with the same weights. Numerical solutions to both problems show the utility of the proposed method for practical applications in different formulations. 

AFNOR Aramid fibre Aspect ratio ASTM ATH Autoclave moulding... 

On the base of the experiments preformed and the test results from other investigators, Shah and Gopalaratnara concluded that SFRC made with weaker matrices, higher fibre contents and larger fibre aspect ratios are more rate sensitive than those made with stronger matrices, lower fibre contents and smaller fibre aspect ratios. Resulting from the comparison between... 

For the data in Figure 4.10(b), the different slopes may be associated with different r]o values, which might be a function of the fibre aspect ratio. 

Figure 7.7 Effect of fibre aspect ratio on the workability of concrete, as measured by the compacting factor [21 ].

Reinforcing fibre Aspect ratio Flexural strength (MPa) Impact toughness (kj/m ) Density (kglrn )... 

The comparisons between different types of fibres that were treated similarly indicate that the composites produced may have a similar flexural strength, but may be quite different in toughness (Table 11.3) [26,29]. These differences cannot be explained on the basis of density (which is similar in all the specimens), or the geometry (aspect ratio) of the fibre, which is highest for the fibre which led to the composite of lowest toughness (Table 11.3). Similar trends were reported by Coutts [30] for softwood and hardwood fibres prepared with room temperature cured matrix. There, the better performance of the softwood fibres was attributed to the higher fibre aspect ratio. 

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