A numerical study on the thermal expansion coefficients of fiber

45
⎡
Ef
⎤
⎢
ν
2
m
2
( )
( 1+
ν )( )
⎥
m
ν
m
−1 C E
m
α = − − ⎢
− ⎥
2
α
m
α
m
αf
(3.24)
⎢1+
1.1υf
2 1 E
f
− ν + +
⎥
⎢
m
2ν
mC
⎣1.1υ
−
⎥
f
1
C E
m ⎦
in which
C
1.1υ
1 −1.1υ
f
= (3.25)
f
3.4.1.9 Equation of Chamis
Chamis (1984) has used a simple force balance, or strength of materials, approach
to derive expression for both mechanical and thermal properties of unidirectional
composites with transversely isotropic fibers. The derived expression for the
longitudinal thermal expansion coefficient is again identical to Schapery’s formula.
The expression for the transverse thermal expansion coefficient is
α
⎛ E
f1
⎞
( 1 − υf
) ⎜1
+ υf
ν
m m
= α υ
⎟ (3.26)
⎝
⎠
2 f2 f + ⎜
α
E1
3.4.1.10 Equation of Sideridis
Sideridis (1994) has calculated the expansion coefficients of the composite using
a model which introduces the concept of the boundary interphase. This concept
determines the influence of the interphase which depends on the quality of adhesion
between fiber and matrix. It has been assumed that the composite has well defined
material properties for the fiber and matrix, whereas the interphase material has
inhomogeneous properties (thermal expansion coefficient, the elastic modulus and
Poisson’s ratio) varying from the fiber surface to the matrix. He also made the
following assumptions: