Load transfer fibre length

It is evident from Fig. 3.29 that there is a minimum fibre length which will permit the fibre to achieve its full load-carrying potential. The minimum fibre length in which the maximum fibre stress, ((rf)maxt be achieved is called the load transfer length, The value of may be determined from a simple force balance... 

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. 

This is the well-known rule-of-mixture which describes a rather idealised situation and can predict the modulus only for continuous fibre-reinforced composites where there is sufficient stress transfer from the matrix to the fibre. However, short fibres are usually much shorter than the specimen length. For short fibres we must consider the matrix-fibre stress transfer. When the matrix is under stress, the maximum stress transferred to the fibre is described by the interfacial stress transfer (t). The stress transfer depends on the fibre length (/), so that at some critical length, /, the stress transferred is large enough to break the fibre. The stress transferred to the fibre builds up to its maximum value (o that which causes breakage) over a distance 1 from the end of the fibre. This means that the long fibres carry load more efficiently than short fibres. 

When instead of continuous fibres, short fibres or wires are used, their efficiency should be accounted for by a coefficient 7] 1.0. Decreased efficiency is caused by the fact that the load is transferred from the matrix to the fibre by bond stress t or friction on the fibre surface. Assuming that stress is uniformly distributed along the fibre length a concept of critical... 

The load transfer between the crack surfaces results in a maximum of the stress in the part of the fibre that is situated within the crack. This stress has to be transferred to the matrix on both sides, in a region whose size is approximately that of the critical fibre length. If the stress in the fibre in this region exceeds the fracture stress, the fibre breaks. Fracture usually occurs at a defect, for example a surface defect or a local reduction in diameter. Because of this, fibre fracture occurs not always directly at the crack surface, but at an arbitrary position between the stress maximum near the crack surface and the region where the fibre stress has decreased markedly. The size of this region is... 

In the following, we consider the case of long fibres with a length several times larger than the critical length (see equation (9.9)). In this case, the fibre is loaded in tension over most of its length, for load transfer occurs only near its end points (see figure 9.6). The fibre will thus fail by fracture. 

Diffusion creep is also important in fibre composites, ft was shown in section 9.3.2 that the load transfer to a fibre is determined only by the aspect ratio, the quotient of length and diameter. That the length is considered to be important in technical applications is only due to the fact that the fibre diameter cannot be made arbitrarily small, whereas the length can be as large... 

These data imply that the fatigue strength is dominated by fibre type, i.e. glass rather than resin type or fibre length (provided the fibres are longer than the minimum length to transfer the load). 

In many simplified treatments of the stress-transfer problem, reference is made to an average interfacial shear stress value, t, assuming a uniform interfacial shear stress distribution aiong the whole fibre length for a pull-out load P,... 

The condition for maximum reinforcement, that is the condition ensuring maximum stress transfer to the fibres, before the composite fails, is to have a length higher than the critical length (Fig. 19.5). If the fibre aspect ratio is lower than its critical value, the fibres are not loaded to their maximum stress value. A specificity of cellulose fibres is their flexibility compared to glass fibres which allows a desirable fibre aspect ratio to be maintained after processing, which is around 100 or 200 for high performance short-fibre composites. 

If the load on the composite is increased, the weakest fibre will break and will thus not transfer any tensile stresses at the position of failure. This fracture, however, will not unload the whole fibre. If it is much longer that the critical length, the load will be transferred by interfacial shear stresses from the matrix to both fibre fragments. At some distance from this region, both fibre fragments bear the same load as before. Near to the fracture position, the material is weakened and the load is transferred to the surrounding material. 

The strength of the fibres must be, of course, effectively utilised by the spun yam. A yam can never have the same strength as its constituent fibres because of the fact that to withstand an applied load, the yam depends on the frictional contact between the overlapping lengths of fibres to transfer the load to all the fibres. The higher the twist the better the frictional contact and the stronger the yam, but for each fibre type there will be an optimum twist to obtain maximum yam strength [8]. 

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