Developments in Ceramic Materials Research

178
M. A. Sheik
During the cooling from a typically high processing temperature of CMCs, very high
thermal stresses ensue as a result of the thermal mismatch between the reinforcement and the
matrix. In the instance of a fibrous composite, an interfacial pressure develops during the
cooling phase. Thermal stresses generated are dependent on the reinforcement volume
fraction ‘V’, reinforcement geometry, thermal mismatch (αF < αM) temperature interval ‘ΔT’
and also the modulus ratio (EF/EM).
Generally, during cooling, the matrix tends to contract more than the reinforcement
putting the reinforcement in compression (αF < αM). This mismatch is difficult to eliminate,
but it can be manipulated to extract desirable characteristics of the composite. Through a
prudent choice of components, it is feasible to acquire a favourable residual stress pattern
rather than adverse final attributes at the end of the processing. In CMCs, crack deflection at
the fibre/matrix interface is beneficial for the augmentation of toughness in the composite.
Frequently, interfacial coatings, that are primarily mechanical in nature, are introduced in
CMCs to optimise stress distribution and bonding at the fibre/matrix interface.
The longitudinal expansion coefficient of a composite is given by:
where:
Similarly, the transverse expansion coefficient of a composite is expressed by:
and ‘V ’ is the volume fraction, ‘E ’ is the Young’s Modulus, ‘ν ’ is the Poisson’s ratio and
the subscripts ‘C ’, ‘F ’ and ‘M ’ refer to composite, fibre and matrix, respectively [13].
For a unidirectional fibre reinforced composite, a prediction of thermal conductivity in
the longitudinal (l) and the transverse (t) directions is proposed by Behrens [14] as:
k 1 = kcl
= k FlVF
+ k MV
k2
= kct
=
k
kFtk
M
V + k V
Ft
f
M
M
M
where, subscripts ‘1’ and ‘2’ denote the principal directions of the unidirectional composite.
In case of woven fabric-reinforced composites, such formulation is not applicable since nonhomogenous
material phases are intermixed and intertwined in one volume. One direct
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