Characterization and control of the fiber-matrix interface in ceramic ...

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5,2 Mechanical Considerations
The prediction of the properties and behavior of a selected
composite system is a formidable challenge.
A composite is a
heterogeneous mixture of multiple phases with differing physical,
chemical, and mechanical properties. The composite properties are
derived from the properties of the constituents and the interaction that
occur between the components. A simple calculation of tensile stress and
strain for a composite containing continuous filament reinforcemeiit can
be based on the following assumptions (24,48-52).
1. The filaments are perfectly aligned parallel to the tensile
axis and surrounded by matrix,
2. Load is transferred from the matrix to the fibers by shear
stresses at the interface.
3. The filaments, the matrix, and the composite are elongated
equally according to Hooke’s Law.
4. The fiber reinforcement is fully bonded to the matrix, and the
fibers all have the same strength, size, arid shape.
5. The stress on the components is determined by the modulus and
the strain.
On this basis, linear expressions for the modulus and strength of a
composite material have been derived from the rule of mlxtures (53).
The
linear models are not as accurate as some of the more complex theories
developed in recent years, but the mathematics is much less rigorous
and general trends and relationships can be examined.
The mechanical
properties of the fiber and the matrix contribute to the final properties