Page 102 - Carbon Nanotube Fibres and Yarns

94 Carbon Nanotube Fibers and Yarns

the modulus between CNT tubes inside a bundle and modulus between
the CNT and the polymer matrix. Once CNTs aggregate into bundles,
CNTs can easily slip between each other and G 12 between CNTs inside
a CNT bundle becomes as low as 1 GPa. Thus, a highly drawn nano-
composite fiber with well-aligned individual CNTs will maximize the
reinforcement effect.

5.4.3 CNT/matrix interfacial shear strength

Stress transfer between CNT and polymer matrix is essential for strength
of CNT-reinforced polymer composite fibers. A typical scheme of a CNT
embedded in polymer matrix is shown in Fig. 5.13. During stretching or
compressing, stress is transferred from the matrix to the CNT. A critical
length (L c ) of CNT is defined as the minimum length required to avoid
CNT being pulled out from the polymer matrix:
σ D
L = CNT CNT (5.2)
c
τ 2 c
where τ c is the interfacial shear strength between the CNT and the polymer
matrix, σ CNT is the CNT strength, and D CNT is the diameter of the CNT.
The critical aspect ratio (R c ) of CNT is therefore:
L σ (5.3)
R = c = CNT
c
D CNT τ 2 c
Fig. 5.13 shows the relationship between R c and τ c of a CNT in polymer
matrix. It is clear that a high strength CNT gives a high R c value. For a

s =20GPa
750 s =30GPa
s =40GPa

500
R c s(x)

250

30 MPa
0 25 50 75 100 125 150
(MPa)
t c
Fig. 5.13 Relationships between R c and τ c . The strength of CNT is assumed to be 20, 30,
and 40 GPa, respectively.