Aligned fibre composites

As shown in Fig. 3.4 stress-strain tests on uniaxially aligned fibre composites show that their behaviour lies somewhere between that of the fibres and that of the matrix. In regard to the strength of the composite, Ocu, the rule of mixtures has to be modified to relate to the matrix stress, o at the fracture strain of the fibres rather than the ultimate tensile strength, o u for the matrix. 

El and E2 refer to the longitudinal and transverse moduli for aligned fibre composites of the type shown in (Fig. 3.29). These values can be determined experimentally or using specifically formulated empirical equations. However, if the fibres are relatively long then equation (3.5) and (3.13) may be used. These give results which are sufficiently accurate for most practical purposes. 

Intuitively, however, the RVE for an amorphous polymer may be expected to be no more than 10 nanometres or so. In an aligned fibre composite with continuous fibres we need to take a sample sufficiently large as to contain perhaps 30 to 50 fibres in a lateral dimension and in this case the coefficient of variation of stress as between fibres would enable a measure to be decided. In a random array of fibres however (chopped strand mat) the RVE must be of the order of a fibre length at least as is also the case for an aligned short fibre composite. 

The Halpin-Tsai model (64) yields, for aligned fibre composites and in conditions where the modulus of the fiber, E(, is much higher than that of the unfilled matrix (as in elastomeric composites) ... 

Figure 10.37 (a) A longitudinal load applied to an aligned fibre composite and (b) a transverse load applied to an aligned fibre composite... 

Longitudinal load on a continuous and aligned fibre composite... 

This approximation is called the Voigt model, and the value of the elastic modulus is often known as the Voigt bound. The expression is identical to that for a continuous aligned fibre composite under a longitudinal load, and gives the elastic modulus when the load is applied parallel to the sheets. Similarly, if the stress is applied perpendicular to the layers, and an iso-stress condition applies (the Reuss model), the elastic modulus is ... 

Fibre matrix coupling in aligned fibre composite (a) coupling for tensile stress parallel to axis 1 and (b) coupling for tensile stress parallel to axis 2. 

Tensile test on aligned fibre composite at angle to axis 1. 

Schematic sketch of tensile stress-strain curves for aligned fibre composite containing brittle fibres in a ductile matrix. Contributions from fibres and matrix are shown as dashed lines (a) low fibre volunte fraction and (b) high 4>,. 

Schematic sketch graph o( tensile strength o-, versus fibre volume fraction lor an aligned fibre composite containing dfaconlinuous brittle fibres in a ductile matrix (dotted lines show the case of continuous fibres, for comparison). 

In aligned fibre composites loading along the fibre direction is unlikely to lead to significant creep problems, while loading off axis to fibre direction may result in excessive deformation. 

Elastic constants of highly aligned fibre composites... 

Consider a perfectly aligned fibre composite reinforced with isotropic fibres of... 

The theoretical considerations outlined above show that a uniaxially aligned fibre composite will show a high degree of mechanical anisotropy, i.e. > G -... 

Fig. 6.18. Schematic sketch graph of tensile strength a versus fibre volume fraction ,for aligned fibre composite containing ductile fibres in a brittle matrix (case II).

Agarwal. B. D. and Broutman, L. J. (1980). Analysis and Performance of Fibre Composites. John Wiley, New York. A relatively advanced text that gives a clear and comprehensible account of the difficult subject of stiffness and strength in aligned fibre composites. (Relevant to Chapters 6 and 8.)... 

Elastic Constants of Highly Aligned Fibre Composites... 

Consider a perfectly aligned fibre composite reinforced with isotropic fibres of infinite stiffness in an isotropic matrix of modulus E and Poisson s ratio v . In the matrix we have... 

There is an extensive literature on composite materials stemming from the seminal papers of Eshelby [8], who considered the elastic field in and around an elliptic inclusion in an infinite matrix. His theory assumed a single particle in an infinite matrix and therefore was valid only for low-volume fractions ( 1%). The extension to more concentrated systems was undertaken by Mori and Tanaka [9], whose method was used by Tandon and Weng [10] to derive the elastic constants of an aligned fibre composite. The composite moduli for this model are given by... 

The fibre volume loading, Vf, is usually between 55 and 65v/o for an aligned fibre composite or laminate. The value may be lower for moulding compounds and GRP and in these cases it is often quoted as a weight percentage. 

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