An Introduction to Composite Materials

The previous three chapters cover the elastic behaviour of composites containing aligned fibres that are, in effect, infinitely long. Use of short fibres (or equiaxed particles) creates scope for using a wider range of reinforcements and more versatile processing and forming routes (see Chapter 15). There is thus interest in understanding the distribution of stresses and strains within such composites, and the consequences of this for the stiffness and other mechanical properties. In this chapter, brief outlines are given of two analytical models. In the shear lag treatment, a cylindrical (short fibre) reinforcement is assumed, with stress fields in fibre and matrix being simplified (leading to some straightforward analytical expressions). It introduces important concepts concerning load transfer mechanisms, although it is not very widely used for property prediction. The Eshelby method, on the other hand, is based on the reinforcement being ellipsoidal (anything from a sphere to a cylinder or a plate): the analysis is more rigorous, but with the penalty of greater mathematical complexity. The model is only briefly described here. Its use also introduces an important concept – that of a misfit strain, which is helpful in areas well beyond those of the mechanics of conventional composite materials.