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Published online by Cambridge University Press: 04 February 2010
Composite materials are inherently inhomogeneous, in terms of both elastic and inelastic properties. One consequence of this is that, on applying a load, a non-uniform distribution of stress is set up within the composite. Much effort has been devoted to understanding and predicting this distribution, as it determines how the material will behave and can be used to explain the superior properties of composites over conventional materials. In this chapter, a brief survey is given of the methods used for modelling stress distributions in composites. These techniques range widely in nature and complexity. Some are more suited to certain types of composite and attention is drawn to areas of particular relevance to metal matrix composites. No treatment is presented in this chapter of the Eshelby method, which is particularly useful for MMCs, since it is considered in detail in Chapters 3 and 4.
The slab model
The simplest way to model the behaviour of a composite containing continuous, aligned fibres is to treat it as if it were composed of two slabs bonded together, one of the matrix and the other of the reinforcement, with the relative thickness of the latter in proportion to the volume fraction of the fibres (designated as f). The response of this ‘composite slab’ to external loads can be predicted quite easily, but its behaviour will closely mirror that of the real composite only under certain conditions (Fig. 2.1).
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