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

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In the analysis of the mechanical relationships that control the
performance of fiber-reinforced materials, it was assumed that a perfect
bond exists between the fiber reinforcement and matrix. The condition
ensures complete load transfer in the system and simplifies the
calculations. The formulations indicate that a high ratio of fiber to
matrix Young’s modulus, Ef/Em, is desirable for ceramic matrix
composites, where the matrix has the lower ultimate strain. As noted
earlier, the moduli of the components of ceramic-ceramic composites are
much closer than in polymer- and metal-matrix systems; therefore, it is
obvious that these expressions do not real-istically explain the behavior
of many brittle matrix composites.
It has been demonstrated that the
failure strain of the matrix can be increased by the addition of fiber
reinforcement and that matrix fracture does not necessarily constitute
the upper limit of load capacity of the composite.
The range in which the linear representations for stress and strain
are accurate is limited by the condition of matrix fracture. The first
deviation from linear behavior occurs immediately upon matrix failure,
and beyond the point of matrix fracture, the mechanical behavior of a
composite is governed by the properties of the fibers and by the adhesion
and frictional stresses at the fi-ber-matrix interface (Figures 6.2 and
6.3). The effect of the fiber-matrx bond on the failure strain of the
matrix in a composite has been examined. Aveston, Cooper, and Kelly
(81,82) developed a model relating the failure strain of the matrix to
material and composite parameters.
The ACK (Aveston, Cooper, and. Kelly) model is based on energetics
and employs an energy balance to predict the point of matrix failure