Analysis of Short Fibre Composites

In order to understand the effect of discontinuous fibres in a polymer matrix it is important to understand the reinforcing mechanism of fibres. Fibres exert their effect by restraining the deformation of the matrix as shown in Fig. 3.28. The external loading applied through the matrix is transferred to the fibres by shear at the fibre/matrix interface. The resultant stress distributions in the fibre and matrix are complex. In short fibres the tensile stress increases from zero at the ends to a value ( r/)max which it would have if the fibre was continuous. This is shown in Fig. 3.29. From the previous section it may be seen that (o /)max may be determined from 

The stress distribution in short fibres is often simplified to the form shown in Fig. 3.29(c) 

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 

The maximum value of it will occur when ( r/)max reaches the tensile strength of the fibre, Ofu, and this is defined as the critical fibre length, Ic 

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. 

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