Strength of Fibre Composites

Up to this stage we have considered the deformation behaviour of fibre composites. An equally important topic for the designer is avoidance of failure. If the definition of failure is the attainment of a specified deformation then the earlier analysis may be used. However, if the occurrence of yield or fracture is to be predicted as an extra safeguard then it is necessary to use another approach. 

In an isotropic material subjected to a uniaxial stress, failure of the latter type is straightforward to predict. The tensile strength of the material will be known from materials data sheets and it is simply a question of ensuring that the applied uniaxial stress does not exceed this. 

If an isotropic material is subjected to multi-axial stresses then the situation is slightly more complex but there are well established procedures for predicting failure. If a,i and Oy are applied it is not simply a question of ensuring that neither of these exceed ar- At values of and Oy below oj there can be a plane within the material where the stress reaches ot and this will initiate failure. 

A variety of methods have been suggested to deal with the prediction of failure under multi-axial stresses and some of these have been applied to composites. The main methods are 

That is, if the local tensile, compressive or shear stresses exceed the materials tensile, compressive or shear strength then failure will occur. Some typical values for the strengths of uni-directional composites are given in Table 3.5. 

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Figure 6.14 Schematic representation showing interlaminar failure of fibre composite substrates arising from the transverse (out-of-plane) tensile stresses, o-ii, which occur due to the eccentricity of the loading path, and the relatively poor transverse strength of fibre composites.

The word "composites" has a modern ring. But using the high strength of fibres to stiffen and strengthen a cheap matrix material is probably older than the wheel. The Processional Way in ancient Babylon, one of the lesser wonders of the ancient world, was made of bitumen reinforced with plaited straw. Straw and horse hair have been used to reinforce mud bricks (improving their fracture toughness) for at least 5000 years. Paper is a composite so is concrete both were known to the Romans. And almost all natural materials which must bear load - wood, bone, muscle - are composites. 

A unidirectional fibre composite consists of 60% by volume of continuous type-1 carbon fibres in a matrix of epoxy. Find the maximum tensile strength of the composite. You may assume that the matrix yields in tension at a stress of 40 MPa. 

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. 

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. 

If the matrix in 3.7 was reinforced with the same volume fraction of glass but in the form of randomly oriented glass fibres rather than continuous filaments, what would be the tensile strength of the composite. The fibres are 15 mm long, have an aspect ratio of 1000 and produce a reinforcement efficiency of 0.25. The fibre strength is 2 GN/m and the shear strength of the interface is 4 MN/m". 

The law of mixtures is classically applied by replacing the strength of the fibres by their contribution to the strength of the composite, and by taking account of the a and coefficients ... 

Figure 6.10 shows schematically the relative positions (modulus versus strength) of some composites according to the nature and form of the fibres. These are examples with different reinforcement contents and forms and the comparison is not really representative of all the possibilities. 

It is also found that there is a general increase in strength of the composites with increasing fibre volume fraction. However, at low values of Vf the strength is below that of the pure resin until sufficient fibres are present to produce reinforcement (29) and at high values of Vf (> 60%) the strength falls off because there is not enough resin to wet the fibres (37). 

The most important effects of the fibre stress falling away to zero at the ends are reductions in the axial tensile modulus and strength of the composite. The effect on modulus can be found as follows. Suppose the fibres are parallel, and a line is imagined drawn across the composite at right angles to them, as in Figure 6.24. The line intersects fibres at... 

A unidirectional carbon fibre-epoxy laminate 3 mm thick is cut into a 10 mm wide strip and subjected to three-point bending with a span of 20 mm. Failure occurs by interlaminar splitting at a load of 2400 N. Calculate the interlaminar shear strength of the composite. 

The effect of the amount of natural fibre such as corn stover, the fibre length and the amount of cross-linker such as divinylbenzene with rm-butyl peroxide on the structure and thermomechanical properties of the soybean and linseed oil-based green composites, revealed that the properties were improved with an increase in the amount of fibre and a decrease in the length of the fibre. Mechanical properties like Young s modulus and the tensile strengths of the composites increased from 291-1398 MPa and 2.1-1 A MPa, respectively for 20-80 wt% fibre loading. However, water uptake also increases under these conditions. The composites contain... 

Hence for the purposes of the EUROCOMP Design Code it is assumed that the strain to failure of the fibres is smaller than that of the matrix and that the matrix can support no load once the fibres reach their failure strain. Therefore Equation (4.58) of the EUROCOMP Design Code is taken as a conservative estimate of the longitudinal strength of the composite. 

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