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

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The stress in the matrix resulting from an applied strain was given
in Eq. (5).
Remembering that u = Ee and substituting Eq. (5) into
Eq. (ll), the thermal mismatch stress in the matrix can be calculated
(61,62) from
Again it can be shown that if ha is positive and AT is large enough, the
thermal stress will exceed the ultimate stress of the matrix and the
matrix will fail. Table 5.2 presents the calculated matrix thermal
stresses for a set of fiber-matrix combinations.
The expressions for interfacial pressure (P) or radial stress at the
fiber-matrix interface can be derived as for the matrix. The resulting
relationship is
Fricti-onal stress transfer occurs when the value is negative, thus af
must be less than am.
Table 5.3 contains the calculated interfacial
pressures for some selected fiber-matrix combinations. The axial stress
experienced by the fibers is given by the the same equation; however,
thermal expansion in many fibers is anisotropic with radial expansion
coeffici.ents differing from the axial values (Table 5.3).
From these relationships, it is shown that fiber-matrix thermal
expansion differences must be kept to a minimum. The difference should
not be negative because the fibers will debond from the matrix and