A numerical study on the thermal expansion coefficients of fiber

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expect the coefficient of thermal expansion of a composite to follow simple law of
mixtures given by:
α = α υ + α υ
(3.6)
c
f
f
m
m
where α c , α f , α m are thermal expansion coefficients of the composite, filler and matrix
respectively and υ f and υ m are the volumetric fractions of the filler and the matrix.
Because of the differences in the thermal expansivities of the phases a state of
micro-stress often exists between them. These stresses influence the thermal
expansion behavior of the body. Thus, its thermal expansion coefficient does not
follow the rule of mixtures.
3.4.1.2 Equation of Thomas
as
Thomas (Sideridis, 1994) put forward an empirical solution which can be written
α = α υ + α υ
(3.7)
a
c
a
f
f
a
m
m
where a may vary from -1 to +1, and γ is the volumetric thermal expansion
coefficient which is defined as α c = 3α for an isotropic composite. However, for a
unidirectional composite, which is isotropic in the two transverse directions, the
relation between volumetric thermal expansion coefficient and longitudinal and
transverse thermal expansion coefficients can be written as
α = α + 2α
(3.8)
c
1
2
where α 1 is the thermal expansion coefficient in the longitudinal direction and α 2 is
the thermal expansion coefficient in the transverse direction. The empirical nature of
the equation makes it suitable for most filed systems by the correct use of the
adjustable constant.