Elasticity of fibre composites

Young s modulus of a fibre composite is determined by the elastic properties of the constituent materials and also depends on the loading direction. Because the fibres are usually stiffer than the matrix, the modulus is larger in fibre direction than transversally to it. 

In this section, we start by considering the simplest case of continuous, uniaxially directed fibres loaded precisely in parallel or transversely to the fibre direction. Afterwards, we will discuss the case of arbitrary load orientation. 

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Compute the modulus of elasticity of a composite consisting of continuous and aligned carbon fibres of 60 % weight fraction in an epoxy resin matrix under (a) longitudinal and (b) transverse loading. The modulus of elasticity of the carbon fibres is 290 GPa and the density is 1785 kg m. The elastic modulus of the resin is 3.2 GPa and its density is 1350 kg m. ... 

Markham, M.F. (1970) Measurement of the elastic constants of fibre composites by ultrasonics. Composites, 1, 145. 

The mechanical properties of plastics materials may often be considerably enhanced by embedding fibrous materials in the polymer matrix. Whilst such techniques have been applied to thermoplastics the greatest developents have taken place with the thermosetting plastics. The most common reinforcing materials are glass and cotton fibres but many other materials ranging from paper to carbon fibre are used. The fibres normally have moduli of elasticity substantially greater than shown by the resin so that under tensile stress much of the load is borne by the fibre. The modulus of the composite is intermediate to that of the fibre and that of the resin. 

To obtain a value of the elastic modulus of a composite in which the fibres are both continuous and aligned parallel to each other, it is simplest to assume that the deformation of the fibres and the matrix is the same, that is, that they are firmly bonded together (Figure 10.37a). This is termed the iso-strain condition, in which case ... 

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 ... 

The value of the elastic modulus, often called the Reuss bound, is identical to that for transverse loading on a fibre composite, and gives a value for the elastic modulus normal to the layers. In both of these equations, E, E and Ep are the elastic moduli of the ceramic, matrix and particles, respectively, and Vc (equal to 1.0), Vm and Vp are the corresponding volume fractions. 

Two concepts from fibre-reinforcement theory are of general use in polymer mechanics. The first is the effect of inclusion shape on the anisotropic elastic moduli of a composite. Two rules control the effects of fibre reinforcement ... 

Tsukrov 1, Novak J. Micromechanical modelling of transverse moduli of unidirectional composites with non-circular elastic fibres. In Brebbia C A, de Wilde WP, editors. High performance stmctures and composites. Southampton, Boston WIT Press 2002. 

The degradation of the composite laminates can be modelled as simple strength criteria for fibres or matrix, before delamination occurs. Eigure 9.19 shows the test force history for a 200 x 200 mm plate and the various numerical EE (77) predictions (Davies et al. [42]), The hnear elastic case does get the time of the event but underestimates the peak force by a factor of 3. The damaged EE prediction overestimates the force but does get the departure from the linear solution correctly. The fuUy degraded solution (with much fibre failure) does match the experimental history. Delamination was confined to one interface near the mid-plane as the C-scan image indicates. 

It should be noted that the composites damage and failure models discussed here are based on an assumption of rate-independent behaviour, and materials properties used for validation studies are based on quasi-static tests. This is currently standard practice in impact simulations of composite structures, which is an important assumption in the work. Reasons for this are the lack of international dynamic test standards for measuring rate-dependent composites properties, so established test procedures are missing. Dynamic failure models for composites are not well understood nor implemented in current commercial FE codes. In justification it should be pointed out that carbon fibres are highly elastic, thus fibre-dominated properties show no... 

Figure 12.21 Plot of the relationship between the predicted unidirectional (UD) carbon fibre composite failure strain and composite length. The data are presented for a viscoelastic TGAP-DDS matrix and a purely elastic matrix. The dotted line represents a typical experimental failure strain for a UD carbon fibre composite [49].

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