Volume fibre

L expression (41) constitue done un test extremement sensible pour verifier d une maniere directe la contribution du volume fibre a la viscosite, et montre la fecondite du concept que nous avons expose. 

Pour les polymdres vitreux, il n existe pas d etudes comparables concernant la variation isotherme de rj. En etudiant la variation isotherme du module complexe de cisaillement, Kovacs, Stratton et Ferry (1963) ont montrd rdcemment que cette variation est intimement liee k celle du volume de l dchantillon. Ils ont estime ainsi que la contribution pure de la temperature k la variation de aT est de l ordre de 20% de la contribution du volume fibre. D autre part, ces auteurs ont montre que le spectre des temps de relaxation subit une modification importante dans le domaine de la transition vitreuse. II semble cependant que pour les verres mineraux, ce spectre reste invariant dans ce meme domaine (Kurkjian, 1963). 

La validite des expressions basees sur le concept du volume fibre peut etre etendue meme a des temperatures voisines et inferieures 4 lorsque aT et s tendent vers I infini (Appendice 1). On peut cependant retrouver l expression integrate correspondant 4 ce cas d une manure plus directe, en se referant k la valeur de t a l instant initial en remplagant dans l eq. (53) f, le seul param tre qui depende du temps, par fi — (v — v)lvoa. D4s lors, en designant tTj ti par rit on a pour les experiences de contraction apr s trempe ... 

A titre d exemple, nous examinerons ici une expression de la variation de Tg pour les systemes binaires (Braun et Kovacs, 1963) qui est bas6e sur le concept du volume fibre de relaxation, 6tant donnee la nature cin ique de la transition vitreuse. 

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... 

Fig. 25.3. The variafion of peak stress with volume fraction of fibres. A minimum volume fraction (VJ ) is needed to give any strengthening.

The number of fibres per unit crack area is 4Vf / Tid (because the volume fraction is the same as the area fraction on a plane perpendicular to the fibres). So the total work done per unit crack area is... 

The properties of a foam are determined by the properties of the polymer, and by the relative density, p/p - the density of the foam (p) divided by that of the solid (p ) of which it is made. This plays the role of the volume fraction Vf of fibres in a composite, and all the equations for foam properties contain p/p. It can vary widely, from 0.5 for a dense foam to 0.005 for a particularly light one. 

A unidirectional fibre composite consists of 60% by volume of Kevlar fibres in a matrix of epoxy. Find the moduli and Comment on the accuracy of your value for E. Use the moduli given in Table 25.1, and use an average value where a range of moduli is given. 

A composite material for a car-repair kit consists of a random mixture of short glass fibres in a polyester matrix. Estimate the maximum toughness of the composite. You may assume that the volume fraction of glass is 30% the fibre diameter is 15 pm the fracture strength of the fibres is 1400 MPa and the shear strength of the matrix is 30 MPa. 

This gives a maximum ratio of 43, which is more than enough. In fact, to bring the anisotropy down to the target figure of 16 we need to reduce the volume fraction of fibres to only 0.13 ... 

This design study has shown that it is possible to design a sectional composite that will reproduce both the vibrational frequencies and the mass of a traditional wooden soundboard. For a soundboard made out of spruce the equivalent composite is a sandwich of cardboard glued between two identical layers of aligned CFRP with a fibre volume fraction of 0.13. If the wooden soundboard is 3 mm thick the replacement composite must be 1.98 mm thick with a cardboard core of 1.25 mm. 

E ll = composite modulus parallel to fibres = composite modulus perpendicular to fibres Vj = volume fraction of fibres E = Young s modulus of fibres E, = Young s modulus of matrix. 

Fillers. Some fillers, such as short fibres or flakes of inorganic materials, improve the mechanical properties of a plastic. Others, called extenders, permit a large volume of a plastic to be produced with relatively little actual resin. Calcium carbonate, silica and clay are frequently used extenders. 

The amount of fibres in a composite is often expressed in terms of the volume fraction, V/. This is the ratio of the volume of the fibres, v/, to the volume of the composite, Vc. The weight fraction of fibres, Wf, may be related... 

If the fibres have a uniform cross-section, then the area fraction will equal the volume fraction, so... 

This is an important relationship. It states that the modulus of a unidirectional fibre composite is proportional to the volume fractions of the materials in the composite. This is known as the Rule of Mixtures. It may also be used to determine the density of a composite as well as other properties such as the Poisson s Ratio, strength, thermal conductivity and electrical conductivity in the fibre direction. 

Example 3.2 PEEK is to be reinforced with 30% by volume of unidirectional carbon fibres and the properties of the individual materials are given below. Calculate the density, modulus and strength of the composite in the fibre direction. 

In addition it may be seen that the strengthening effect of the fibres is only observed (i.e. a u > volume fraction is greater than a certain... 

Fig. 3.7 shows how the longitudinal and transverse moduli vary with volume fraction for a unidirectional fibre composite. 

Example 3.17 Short carbon fibres with a diameter of 10 fim are to be used to reinforce nylon 66. If the design stress for the composite is 300 MN/m and the following data is available on the fibres and nylon, calculate the load transfer length for the fibres and also the critical fibre length. The volume fraction of the fibres is to be 0.3. 

In order to get the best out of fibre reinforcement it is not uncommon to try to control within close limits the fibre content which will provide maximum stiffness for a fixed weight of matrix and fibres. In flexure it has been found that optimum stiffness is achieved when the volume fraction is 0.2 for chopped strand mat (CSM) and 0.37 for continuous fibre reinforcement. 

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