materials have their microstructure designed in terms of their macroscopic
constituents, e.g. fibers in a homogeneous matrix material. By controlling
the choice of fibers, their volume fraction, and alignment, the mechanical
properties may be tailored to meet specific design requirements. This is
a different level of control than that available for homogeneous materials.
diagram (a) shows a 'uniaxial fiber-reinforced' composite material
loaded in the fiber direction. For the continuous fibers shown, the strain
is the same in the matrix and the fiber, an isostrain situation. In (b) is shown
how the stress on the composite is carried by the fibers and the matrix.
Normally, the selected fiber material has a larger Young's modulus than the
matrix and for equal elastic strain the fiber stress is higher than the matrix
stress. The Young's modulus of the Composite is given by the 'rule of mixtures'
= EF VF + EM VM ,
the volume fractions of fibers and matrix respectively, also ( VM +
VF ) = 1
= (1 - VF ). The elastic modulus along the fiber
direction can, therefore, be controlled by selecting the volume fraction of