Strength of Aligned Continuous Fibre Composites

Fibres Fail First

We shall now consider the case where the matrix is ductile and the elastic strain to fracture in the fibres is less than the elastic/plastic extension of the matrix as would occur in fibre reinforced metal matrix composites or thermoplastic matrix composites. At low volume fractions of fibres, the chain of events is analogous to the case where the matrix fails first in that the fibres will break and the load will transfer to the matrix which, having a reduced cross-section, will see a sudden jump in stress. Again, what happens next depends on the magnitude of the increase in the stress in the matrix - will it fracture or won't it? The stress on the composite at the point of fibre fracture (ef) is
The force on the composite is just the product of the stress and the cross-sectional area, so the stress on the matrix after the fibres break is
So the stress on the matrix increases by . If the rise in stress is not sufficient to fracture the matrix then it will continue to support the applied load. Thus the fracture strength of the composite will be given by
where sm is the ultimate tensile strength of the matrix; i.e. the addition of fibres leads to a reduction in the strength of the composite to levels below that of the unreinforced matrix. Fortunately, as the fibre volume fraction increases, the fibres carry more of the applied load. When the fibres break, the load transferred to the matrix is large and the much reduced cross-sectional area of the matrix will be unable to support the load and the matrix too will fail. The strength of the composite, like the previous example, is determined by the strength of the fibres i.e.
We can plainly see that the tensile strength of a composite in which the fibres fail at a lower strain that the matrix initially decreases below that of the matrix alone, reaches a minimum and thereafter increase. The is, therefore, a minimum volume fraction, fmin, of fibres that must be added in order for the composite to have a strength at least equal to that of the matrix alone, i.e.,
In the example shown above, where glass fibres are used to reinforce a polyAmide matrix, fmin is around 9%.
Use the applet below to explore the effect that matrix type (brittle/ductile) has on the variation of composite strength with increasing fibre content. . The strength is calculated at the lower strain of
  1. the fibre fractures, or
  2. the (ductile) matrix yields, or
  3. the (brittle) matrix fractures.

Transverse Strength

So far we have only considered the strength of the composite when loaded in a direction parallel to the fibres. However, if the composite is loaded in a direction perpendicular to the fibres then a different set of rules apply - just one of the problems associated with analysing anisotropic materials.
We should recall, that when loaded in the transverse direction, both the fibres and the matrix experience the same stress - so to determine what the strength is we need only look at the weakest link in the composite. Of the two materials that make up the composite, the matrix is invariably the weaker material and so fracture will occur when the stress reaches the matrix fracture stress - or will it? Up to now we have assumed that the join between the matrix and the fibre is perfect and will transmit all the load applied to it. A great deal of effort goes into the engineering of the fibre matrix interface either to make it strong or to deliberately weaken it, depending on the application. We will discuss the fibre matrix interface in a latter class but for now it is safe to assume that the interface is always the weakest link, therefore err on the safe side and set the transverse strength to some fraction of the matrix strength - the exact value can be determined most easily by experiment. Continue with the effects of fibre orientation on strength...