# Effects of CNT Diameter on the Uniaxial Stress-Strain   Behavior of CNT/Epoxy Composites

Authors: N. Yu; Y. W. Chang
Journal: Journal of Nanomaterials
 (2008)

---

## Abstract

The present work studies the effects of the diameter of carbon nanotube (CNT) as well as CNT weight fraction on the uniaxial stress-strain behavior, stiffness, and strength of CNT-reinforced epoxy-matrix composites. The experimental results show that average Young's moduli of 5 wt%-CNT/epoxy composites with a CNT diameterD<20 nm and D=40∼60 nm are 4.56 GPa and 4.36 GPa, and the average tensile strengths are 52.89 MPa and 46.80 MPa, respectively, which corresponds to a percentage increase of 61.1%, 54.1%, 106%, and 82.3%, respectively. Two micromechanics models are employed and the predicted Young's moduli are benchmarked with the experimental data of MWCNT-reinforced epoxy-matrix composites.


---

## Body

## 1. Introduction

In view of its excellent stiffness and strength, the carbon nanotube
(CNT) is considered as an ideal candidate for the reinforcement in composites. Andrews et
al. [1] added 5 wt% single-walled carbon nanotubes (SWCNTs) in isotropic
petroleum pitch. The elastic modulus of SWCNT/petroleum increased from 34 GPa
to 78 GPa, whereas the tensile strength increased from 490 MPa to 850 MPa. Jia et al. [2] used AIBN, a free radical
initiator, and Gong et al.
[3] used the surfactant dodecylether (C12EO8) as a processing aid to improve the interfacial bonding between multiwalled
carbon nanotubes (MWCNTs) and the matrix. The
tensile test results of Allaoui et al.
[4] reported that Young's modulus and
the yield strength were doubled and quadrupled for MWCNT/epoxy composites with
1 and 4 wt% CNTs, respectively, in comparison with those of pure epoxy samples.
However, the three-point bending test results by Lau et al. [5] indicated that the flexural
strengths of all CNT composites were relatively lower than the pure epoxy
sample. The nanoindentation results by Li et al. [6] using an atomic
force microscope showed an increase in elastic modulus by 75% and hardness by
30% in the epoxy reinforced by 5 wt% SWCNTs in comparison with those of neat epoxy. Song and Youn [7] reported that the tensile
strength of epoxy filled with well-dispersed CNTs increased as the CNT weight
fraction increased, yet that of the composite filled with poorly-dispersed CNTs
decreased. Thostenson and Chou [8] used a microscale twin-screw extruder to
align MWCNTs in polystyrene composite films. The interface between CNT and
matrix was studied by Schadler et al.
[9], Ajayan et al. [10], and Cooper
et al. [11]. CNTs were also used
as reinforcements in ceramic- or metal-matrix composites [12–15].In the present work, MWCNTs with a variety of weight fractions and
diameters are added into epoxy and the composites are subjected to uniaxial
tensions. The mechanical properties of composites containing CNTs at the same
weight fraction, yet different CNT diameters, are compared and, therefore, the
effects of CNT diameter on Young's modulus and tensile strength of MWCNT/epoxy
composites are characterized.


## 2. Experiments

As received MWCNTs purchased from
Desunnano Co. in
specific weight fraction (1 wt%, 2 wt%, 3 wt%, 4 wt%, and 5 wt%) are mixed with
7.5 mL epoxy resin E-120 together with 2.5 mL associated hardener
H-100. It is noted that the resin-to-hardener
volume ratio is kept at 3:1. The mixture is first sonicated for 10 minutes and
then stirred amply for 5 minutes. The sonication-stirring step is repeated
three times in order to ensure the uniform distribution and the separation of
the entangled MWCNTs. The nanotube/epoxy mixtures are then poured
into an aluminum mold, vacuumed in an oven for 30 minutes, and then released to
the atmosphere for 10 minutes. This step is repeated two
times in order
to remove air bubbles from the mixtures. The mixture is then
cured in atmosphere. After simple machining, the specimen is ready for
test; see Figure1. The dimensions of the specimen follow ASTM D638 Type IV. In the present work, there are pure
epoxy and composites with 1 wt%-, 2 wt%-, 3 wt%-, 4 wt%-, and 5 wt%-MWCNTs with
their diameters being less then 20 nm or between 40 to 60 nm. The weight
fraction Wt% of CNTs is
given by(1)Wt%=WCNTWCNT+We+Wh×100%, where WCNT, We, and Wh are the weight of the
carbon nanotubes, epoxy resin, and hardener in grams, respectively. Three
specimens for each of the group-neat epoxy, 1 wt%-, 3 wt%-, and 5 wt%-MWCNT/epoxy,
and only one specimen for the group 2 wt%- and 4 wt%-MWCNT/epoxy is prepared. The total number of samples is twenty five.
If the dispersion of MWCNTs is uniform in the epoxy resin, the composite specimen
can be regarded as isotropic. The testing of
the composites follows the ASTM D638 standard tensile test. The grip of
the microcomputer tensile tester (Model No. H-10KS, Hounsfield Test Equipment
Co.) can be controlled in such a manner that the relative displacement rate of
the grips is 1.0 mm/min so that the test can be regarded as quasistatic.Figure 1
MWCNT/epoxy specimen.At the
time of measurement, a resistance-type (120 ohms) strain gage is pasted on the
surface of the specimen in the axial direction. The elastic modulus of MWCNT/epoxy
composite is determined by calculating the slope of the linear portion of the
stress-strain curve.


## 3. The Models

In the present work, two micromechanics models, Eshelby
[16] and Mori-Tanaka [17], are employed to predict Young's
modulus of epoxy reinforced by randomly distributed MWCNTs. The former ignores the interaction between CNTs
and gives the effective elastic constants [C¯] of the composite as follows:(2)[C¯]=[CM]+VI([CI]−[CM])[X], where [CM] is the stiffness matrix of the matrix, [CI] is the stiffness matrix of CNT, VI is the CNT volume fraction, and [X] is given
by [18](3)[X]=12π∫0πdϕ∫0π[Φ]−1([CM]−[CI])−1[CM]×(([CM]−[CI])−1[CM]−[S])−1×[Φ]sinθdθ with [S] being the Eshelby tensor, which is a function
of the geometry of CNT and the elastic properties of the matrix, and [Φ]
being given by
(4)[Φ]=[cos2θsin2θcos2ϕsin2θsin2ϕsin2θsinϕcosϕsinθcosθsinϕsinθcosθcosϕsin2θcos2θcos2ϕcos2θsin2ϕcos2θsinϕcosϕ−sinθcosθsinϕ−sinθcosθcosϕ0sin2ϕcos2ϕ−sinϕcosϕ000−2cosθsinϕcosϕ2cosθsinϕcosϕcosθ(cos2ϕ−sin2ϕ)−sinθcosϕsinθsinϕ0−2sinθsinϕcosϕ2sinθsinϕcosϕsinθ(cos2ϕ−sin2ϕ)cosθcosϕ−cosθsinϕ−2sinθcosθ2sinθcosθcos2ϕ2sinθcosϕsin2ϕ2sinθcosθsinϕcosϕsinϕ(cos2θ−sin2θ)cosϕ(cos2θ−sin2θ)].
Moreover, the
Mori-Tanaka model considering the interaction between CNTs to a certain extent gives
(5)[C¯]=[CM]+VI([CI]−[CM])(VI[I]+(1−VI)[X]−1)−1.


## 4. Results

In the present work, neat epoxy, 1 wt%-, 2 wt%-, 3 wt%-, 4 wt%-, and 5 wt%-MWCNT/epoxy composite specimens where MWCNTs
exhibit two groups of diameters,D: (i)
less than 20 nm and (ii) between 40 and 60 nm, are used. Typical stress-strain curves of MWCNT/epoxy
composites, where CNT diameter D<20 nm is shown in Figure 2 while those of MWCNT/epoxy composites with CNT
diameter D being 40 ~60 nm could be
seen in Figure 3. The composite strength, modulus of elasticity, and fracture
strain data are listed in Table 1. The relationship between composite tensile
strength and CNT weight fraction is shown in Figure 4 and that between Young's
modulus and CNT weight fraction is shown in Figure 5. The
experimental results show that the average tensile strength of 1 wt%-, 2 wt%-,
3 wt%-, 4 wt%-, and 5 wt%-MWCNTs/epoxy with a CNT diameter D<20 nm increases 66.1%, 79.3%, 87.1%, 99.1%, and 106.0%, and average
Young's modulus increases 28.6%, 47.7%, 52.3%, 55.1%, and 61.1%, respectively.
By adding MWCNTs of the same weight fraction with a larger diameter (D=40∼60 nm), the average tensile
strength of 1 wt%-, 2 wt%-, 3 wt%-, 4 wt%-, and 5 wt%-MWCNTs/epoxy increases
42.7%, 51.8%, 65.6%, 78.3%, and 82.3%, and average Young's moduli increase 22.6%,
32.2%, 44.9%, 50.5%, and 54.1%, respectively, compared with average Young's
modulus (2.83 GPa) and the average tensile strength (25.67 MPa) of the neat
epoxy specimens. Adding MWCNTs into epoxy does increase the mechanical
properties of the composites, and the smaller the CNT diameter is the higher
the composite stiffness and strength are.Table 1
Tensile strength, Young's modulus, and fracture strain of CNT/epoxy composites.
Average tensile strength of CNT/epoxy composites (percentage increase)CNT weight percentageCNT diameterD<20 nm (MPa)D=40∼60 nm (MPa)0 (neat epoxy)25.67±0.281 wt%42.64±1.47 (66.1%)36.63±1.06 (42.7%)2 wt%46.03 (79.3%)38.97 (51.8%)3 wt%48.02±1.46
(87.1%)42.52±1.47
(65.6%)4 wt%51.10 (99.1%)45.78 (78.3%)5 wt%52.89±0.79
(106%)46.80±0.51
(82.3%)Average Young's modulus of CNT/epoxy composites (percentage increase)CNT weight percentageCNT diameterD<20 nm
(GPa)D=40∼60 nm
(GPa)0
(neat epoxy)2.83±0.221 wt%3.64±0.20
(28.6%)3.47±0.15
(22.6%)2 wt%4.18 (47.7%)3.74 (32.2%)3 wt%4.31±0.21 (52.3%)4.10±0.17 (44.9%)4 wt%4.39 (55.1%)4.26 (50.5%)5 wt%4.56±0.21 (61.1%)4.36±0.20 (54.1%)Average fracture strain of CNT/epoxy composites (percentage increase)CNT weight percentageCNT diameterD<20 nmD=40∼60 nm0 (neat epoxy)0.87±0.091 wt%1.19±0.11 (36.8%)1.16±0.06 (33.3%)2 wt%1.11 (27.6%)1.05 (20.7%)3 wt%1.15±0.01 (32.2%)1.05±0.11 (20.7%)4 wt%1.20 (37.9%)1.08 (24.1%)5 wt%1.18±0.11 (35.6%)1.10±0.03 (26.4%)Figure 2
Stress-strain curve of MWCNT/epoxy with CNT diameterD<20 nm.Figure 3
Stress-strain curve of MWCNT/epoxy with CNT diameterD=40∼60 nm.Figure 4
Relationship
between composites tensile strength and CNT weight percentage.Figure 5
Relationship between the composites of Young's modulus and CNT weight percentage.The fracture surface of a 5 wt%-CNT/epoxy specimen, where the diameter of CNTs is less
than 20 nm is examined using field-emission scanning electron microscopy and is
shown in Figure6. The dispersion of the CNTs is uniform, which contributes to
the improved mechanical properties of CNT-based composites [8].Figure 6
The fracture surface of 5 wt%-MWCNT/epoxy specimen (DCNT<20 nm).The following elastic properties of a single-crystal
graphite sheet (i.e., a graphene) are used in the microstructure-based double-inclusion
model developed by Yu et al.
[19] to determine Young's modulus of MWCNT as follows:(6)[C]=[1060151800001536.5150001801510600000004.50000004400000004.5]GPa, where the x1-x3 plane is the plane of
isotropy of a graphene. Poisson's ratios of the graphene are v12=0.01, v23=0.2, and v13=0.2 [20]. Since
two ranges of CNT diameters (D=40∼60 nm and D<20 nm) are used in our
specimens, the diameters of two groups of MWCNTs are taken as 50 nm and 15 nm,
respectively, in the present models. The double-inclusion model [19] gives
Young's modulus of an MWCNT with a diameter of 50 nm as 770 GPa, and 1015 GPa
for MWCNT with a diameter 15 nm, which is consistent with the available
experimental data [21]. Young's modulus of epoxy Em is 2.83 GPa and the Poisson's ratio, vf, of the CNT is assumed to
be 0.2 and that of epoxy, vm,
is 0.32. Since the density of MWCNT and that of epoxy are 2.1 g/cm3 and 1.07 g/cm3, respectively; the CNT
volume fractions are 0.51% (1 wt%), 1.03% (2 wt%), 1.55% (3 wt%), 2.08% (4 wt%), and 2.61% (5 wt%). The lengths of the as received MWCNTs range
between 5 and 15 μm, thus the lower and upper bounds on the aspect ratio a1/a2 of MWCNT are roughly estimated as 100∼300 and 300∼1000 for the two groups
of MWCNTs in our calculations. The predicted values are compared with the
experimental data in Figures 7 and 8 for the two groups of CNT diameters D=40∼60 nm and D<20 nm,
respectively. The curves in Figures 7 and 8 give the prediction on Young's moduli
of the composites reinforced by CNTs with a constant aspect ratio. The
experimental data are from specimens reinforced by CNTs with aspect ratios
varying in a certain range and, therefore, are not expected to follow the trend
of any specific curve in Figures 7 and 8. However, the experimental data indeed
fall within the curves corresponding to the predictions based on the lower and
upper bounds on CNT aspect ratio.Figure 7
Predicted Young's modulus compared with the experimental data of the MWCNT/epoxy
compositeDCNT=40∼60 nm.Figure 8
Predicted Young's modulus compared with the
experimental data of the MWCNT/epoxy compositeDCNT<20 nm.


## 5. Conclusion

In the present work, six groups of specimens—neat epoxy, 1 wt%-, 2 wt%-, 3 wt%-,
4 wt%-, and 5 wt%-MWCNT/epoxy composites—are prepared and tested. Furthermore, MWCNTs with
a diameterD (i) less than 20 nm and (ii) between 40 and 60 nm are used in each
of the five groups of composites. The tensile test results show that the
average tensile strength of 5 wt%-MWCNT/epoxy with a diameter D<20 nm increases 106.0%, and average
Young's modulus increases 61.1%. When the same weight fraction of MWCNT with a
larger diameter D=40∼60 nm is
added into epoxy, the average tensile strength of 5 wt%-MWCNT/epoxy increases
82.3%, and average Young's modulus increases 54.1%, compared with those of neat
epoxy, of which the tensile strength is 25.67 MPa, and Young's modulus is 2.83 GPa. The FESEM observation shows the uniform
dispersion of MWCNTs in epoxy resulting in improved mechanical properties of
MWCNTs/epoxy composites. Despite the fact that it is not easy to characterize
CNT aspect ratio, which are roughly estimated in our models, the experimental
data indeed fall within the curves corresponding to the predictions given by
Eshelby and Mori-Tanaka models based on the lower and upper bounds on CNT
aspect ratio.



---

*Source: 834248-2009-01-13.xml*