Carbon Nanotube Reinforced Composites: Metal and Ceramic ...

104j 4 Mechanical Characteristics of Carbon Nanotube–Metal Nanocomposites
Experimental results of tensile measurements are then compared or correlated with
such theoretical models.
The micromechanical models for discontinuously fiber-reinforced composites are
briefly discussed here. The mechanical properties of such composites are mainly
controlled by the stress transfer between the reinforcing fibers and the metal matrix at
the interface. The strengthening mechanism through load transfer from the matrix to
the reinforcement can be estimated from the shear-lag model. Cox originally
proposed this approach where discontinuous fibers were embedded in an elastic
matrix with a perfectly bonded interface and loaded in tension along the fiber
direction [6]. Further, load transfer depends on the interfacial shear stress between
the fiber and the matrix. The Cox model incorporates the aspect ratio (S ¼ l/d where l
is the fiber length and d is the fiber diameter) of the reinforcement into the rule of
mixtures. The Young s modulus of the composite then takes the following form:
E ¼ h lEf Vf þ Emð1 Vf Þ ð4:1Þ
where Ef is the fiber modulus, Em the matrix modulus, Vf the fiber volume fraction
and hl is defined by the following equation:
h l ¼ 1
tan hðbSÞ
bS
b represents a group of dimensionless constants:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2Em
b ¼
Ef ð1 þ umÞlnð1=Vf Þ
ð4:2Þ
ð4:3Þ
where um is the Poisson s ratio of matrix. The Cox model gives a poor prediction of
the strengthening effect of discontinuously reinforced composites because the
contribution of the load transfer effect at the fiber ends is not known. Nardone and
Prewo [7, 8] modified the shear-lag model by taking the effect of tensile load transfer at
the short fiber ends into consideration. Accordingly, the yield strength of a composite
is expressed as:
sc ¼ Vf smS
2 þ sm ð4:4Þ
where Vm denotes the matrix volume fraction and sm the matrix yield strength
For the fiber with a misorientation angle q with respect to the loading axis,
Ryu et al. [9] demonstrated that the S parameter should be replaced by an effective
aspect ratio (Seff) for misaligned fiber. The modified yield strength of composite is
given by the following equation:
sc ¼ Vf smSeff
2
Seff ¼ Scos 2 q þ
þ sm: ð4:5Þ
3p 4
3p
1 þ 1
S sin2 q: ð4:6Þ