Page 411 - Wind Energy Handbook

BLADES 385

rules. Thus, for a ply reinforced by UD fibres, the longitudinal stiffness modulus,
E 1 , can be derived accurately from the rule of mixtures formula

E 1 ¼ E f V f þ E m (1 V f ) (7:3)

where E f is the fibre modulus (72.3 GPa for E-Glass), E m is the matrix modulus (in
the range 2.7–3.4 GPa) and V f is the fibre volume fraction. On the other hand, the
inverse form of this formula, e.g.,

1 (1 V f ) V f
¼ þ (7:4)
E 2 E m E f
significantly underestimates the transverse modulus, E 2 , and the in-plane shear
modulus, G 12 . More accurate formulae based on more sophisticated models are
given in Barbero (1998).
The longitudinal tensile strength of a ply reinforced by UD fibres, ó 1t , can be
estimated from:

E m
ó 1t ¼ ó fu V f þ (1 V f ) (7:5)
E f
where ó fu is the ultimate tensile strength of the fibres. However, the tensile
strengths of E-glass single fibres (3.45 GPa) cannot be realized in a composite, where
fibre strength reductions of up to 50 percent have been measured. Accordingly, a
value of ó fu of 1750 MPa should be used in Equation (7.5).
The longitudinal compressive strength of a ply reinforced by UD fibres is always
significantly less than the tensile strength because of microbuckling of the fibres,
which is governed by the shear strength of the matrix and the degree of fibre
misalignment. A strength reduction of at least 15 percent should be allowed for,
assuming minimum fibre misalignment.
Clearly, longitudinal stiffness and strength are both limited by the fibre volume
fraction obtainable. For hand lay-up, fibre volume contents of 30–40 percent are
typical, but the use of ‘vacuum bagging’, in which trapped air and excess volatile
compounds, such as residual solvent, are extracted, consolidates the composite and
allows a volume fraction of 50 percent or more to be achieved. The use of ‘pre-
pregs’, which are unidirectional fibres or woven fabric pre-impregnated with
partially cured epoxy resin, results in similar increased fibre volume fractions.

Fatigue properties

When expressed in terms of stress, the fatigue properties of composite laminates
extend over a wide range, depending on fibre volume fraction and the number of
plies with fibres in the longitudinal direction. However, data from constant stress
amplitude fatigue test results become much more intelligible if stress ranges are
converted into initial strain ranges, allowing the fatigue properties of composites
with different lay-ups to be compared. (The Young’s modulus of a composite