Fibre parallel load

There is a simple way to estimate the modulus of a fibre-reinforced composite. Suppose we stress a composite, containing a volume fraction Vfo( fibres, parallel to the fibres (see Fig. 6.3(a)). Loaded in this direction, the strain, e , in the fibres and the matrix is the same. The stress carried by the composite is... 

The loading direction is parallel (0°) to the fibres The loading direction is perpendicular (90°) to the fibres... 

We want to calculate Young s modulus of a fibre composite loaded in parallel and perpendicular to the fibre direction (see sections 9.2.1 and 9.2.2). We start by considering a polymer matrix composite with perfectly aligned, infinitely long, uniaxial fibres. 

Example 3.8 A thin unidirectional carbon fibre composite is loaded as shown in Fig. 3.14 and has the properties listed below. If the fibres are aligned at 35° to the x-axis, calculate the stresses parallel and perpendicular to the fibres. 

Fig. 14 The four normal stresses and the four shear stresses acting on a domain resulting from a tensile stress on the fibre. A crack is drawn parallel to the chain direction. The angle in the loaded state between the domain axis and the fibre axis is 6... 

Fracture process in multidirectional composite laminates subjected to in-plane static or fatigue tensile loading involves sequential accumulation of damage in the form of matrix cracks that appear parallel to the fibres in the off-axis plies, edge delamination and local delamination long before catastrophic failure. These resin dominated failure modes significantly reduce the laminate stiffness and are detrimental to its strength. 

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 elastic mechanical properties of carbon fibre-reinforced laminates are highly dependent on the properties of the fibres and the matrix chosen and on the direction of loading relative to the fibre orientation. In a unidirectional laminate, with all fibres orientated in one direction and loaded parallel to the fibres, the properties are mainly dependent on those of the fibres and can be estimated by the rule of mixtures, taking into account the volume fractions of the fibres and the matrix. Equation [5.1] shows that E, the Young s modulus parallel to the fibres is simply given by... 

The ends of the microfibrils create about Itf m point vacancies in the microfibrillar superlattice (Fig. 11). Under applied tensile load they may fail first, eventually by microcrack formation so that the adjacent microfibrils have to carry a heavier load than the rest of the sample. Hence they are first candidates for rupture detectable by the rascals formed at the rupture of tie molecules in at least one amorphous layer of the microfibril affected. Depending on the ratio of axial strength to lateral adhesion of the microfibrils the microcracks will grow parallel (high ratio) or perpendicular (low ratio) to the fibre axis yielding a large number of broken, chains and radicals in the former and a small one in the latter case. Nylon is an example of the former and linear polyethylene of the latter type. 

In tensile loading of a specimen, the maximum shear stresses occur on planes with their normals at 45° to the tensile stress direction. In tensile loading of a 45° specimen we are interested therefore in laminar shear on planes with their normals parallel to the sheet surface which either contain or are perpendicular to the fibre axis i.e. are at 45° to the tensile stress direction). Since easy shear on either set of planes is consistent with the observed high value of S44, additional measurements (such as X-ray diffraction) must be made during deformation in order to determine the relative importance of the possible molecular deformation modes. Such measurements were not attempted in the above study. 

By contrast, when a stress acts in the 2-3 plane, the matrix plays a crucial load-bearing role. Fibres and matrix are now coupled approximately in series , as shown in Figure 6.11(b) for the case of a tensile stress 0-2 parallel to axis 2. The whole tensile force is assumed to be carried fully by both the fibres and the matrix. The tensile stresses in fibres and matrbc o-fj and o- 2 are therefore equal to each other and to the overall stress in the composite ... 

We turn now to the important question of how the composite fails under load. Consider the case in which a tensile stress acts parallel to the fibres (axis 1). The sequence of events varies, depending on which of the two components is the more brittle fibres or matrix (see Figure 6.15). Denoting fracture by an asterisk, the question is which of e and is the smaller We consider the two cases in turn. 

The high strengths predicted are realized only when loads are parallel to the fibres. The composite is much weaker under stress in other directions. This is because cracks seek out the easiest path along which to propagate. In a fibre-reinforced polymer, the easiest paths are through the matrix and along the fibre-matrix interface. 

Special cases exist when has limiting values. When 00 this method models continuous systems of fibre and matrix materials stacked parallel to the load direction. This idealisation, which is known to be accurate, can be used to determine Ei and V12. 

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