Modified embedded atom method study of the mechanical properties of carbon nanotube reinforced nickel composites Page: 6
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PHYSICAL REVIEW B 81, 104103 (2010)
0 0.40 .....
.- - - --
i 0.30 - ---
0.25 - -----------(------ y (H iglt---
'0''CC) 141 SWCCyT S'0 N''SV O'T.)NalK1105 NiIMCNT
FIG. 4. (Color online) Calculated Poisson's ratio (v) for fcc Ni
and Ni/CNT composites with low and high CNT volume fractions.
longitudinal direction (the direction of CNT alignments), E11
(E11) show a dramatic increase and follows the trend
Ni/SWCNT(5,0) < Ni/SWCNT(10, 0)
< Ni/SWCNT(15,0) < Ni/MWCNT.
These increases depend on the CNT volume fractions of the
composites and approximately proportional to the CNT vol-
ume fractions. Similar trend is seen for E22 (E2) and E33
(ET3). For SWCNTs, a slight but gradual decrease is seen for
the E values depending on the CNT diameter and volume
fractions. Interestingly, ET2 and ET increases for Ni/
MWCNT. For example, in this case, E22(or ET3) is increased
by 2 GPa for low CNT volume fraction and an average of 8
GPa for high CNT volume fraction, respectively, which sug-
gests that Ni/CNT composites with significantly larger
MWCNT diameter and with high CNT volume fractions
might increase the Young's modulus in both longitudinal and
transverse directions. However, verification of this hypoth-
esis is beyond the scope of the present paper.
Figure 4 shows the calculated Poisson's ratio, v, for Ni
and the Ni/CNT composites. Our predicted value for pure fcc
Ni is 0.374. Several unique Poisson's ratios can be defined
for the composites depending on the orthogonal directions of
the unit vector along the longitudinal direction and the trans-
verse directions of the composites: (1) v12 and vL3 involve
the strains between the longitudinal direction and the trans-
verse directions. Here, a uniaxial strain is applied in the lon-
gitudinal direction while the transverse directions respond to
this freely. Usually this indicates contraction in the trans-
verse direction during longitudinal elongation; (2) vT2 and
T3 are similar to 3 and , however, in this case a uniaxial
strain is applied in the transverse direction while response
(contraction) is expected in the longitudinal direction; and,
(3) in vT3 both transverse directions are involved, however, a
uniaxial strain is applied in one transverse direction and con-
traction is seen in the other transverse direction. Note, since
similar values are found for v2 and 43, as well as vT2 and
T3, we show an average values for these.
crystal) and Voigt (assuming uniform strain) as follows:
From Fig. 4, the following trends are seen: (1) 12 or 13
show slight variation across the different Ni/CNTs systems
starting from Ni/SWCNT(5,0) in the left to Ni/
SWCNT(15,0) and Ni/MWCNT on the right. In the compos-
ites with high CNT volume fraction, slight decrease is seen
from left to right depending on CNT diameters. The largest
decrease is seen for Ni/MWCNT. In this case, for high CNT
volume fractions, v12 or 13 are found to be 0.34, a value
only marginally smaller than that of 0.37 of Ni. (2) In vT2 or
T3, a significant and rapid decrease is seen across for the
Ni/CNT systems studied (left to right in Fig. 4). Composites
with high volume fraction show a far larger decrease. The
Ni/MWCNT nanocomposites show larger decrease than any
of the Ni/SWCNT composites. For example, for Ni/CNTs
with a high CNT volume fraction, the vT2 (or v3) is found to
be 0.31, 0.26, 0.22, and 0.18, for Ni/SWCNT(5,0), Ni/
SWCNT(10,0), Ni/SWCNT(15,0), and Ni/MWCNT, respec-
tively. An interesting difference in trend is seen between the
longitudinal v 12 (or 13) and the transverse v12 (or vT3). Here,
CNT volume fractions dependency is seen for both of these,
a much steeper decrease is seen for vT2 (or vT3) across the
Ni/CNTs. (3) For 23, a large but gradual increase is seen
across the Ni/CNTs, which depend on the CNT diameters.
This increase is also found to be CNT volume fraction de-
pendent, with a larger increase for composites with high vol-
ume fractions. The variations in vT3 indicate how Ni/CNTs
with different kind of CNTs would respond when an uniaxial
strain is applied along one transverse direction while other is
being freely contracted. The significantly larger changes in
v2 (or v13) and vT3 indicate that these composites have mark-
edly different behavior along longitudinal and transverse di-
rections when uniaxial strain is applied.
For all composites, the calculated shear modulus (G) for
single crystals decrease compared to nickel. For composites
with high CNT volume fractions, a larger decrease is seen as
compared to those with low volume fractions. For Ni/
SWCNT, both G23 and G13 or G12 decrease with increasing
2. Polycrystalline elastic moduli
Real materials are usually polycrystalline aggregates of
randomly oriented single-crystal grains, each exhibiting
single-crystalline elastic properties. These materials exhibit
isotropic properties. The elastic moduli of polycrystalline Ni/
CNT aggregates were computed by averaging appropriate
single-crystal constants (ci) using the expressions of Voigt5o
and Reuss.' These expressions provide upper and lower
bounds for the averaged bulk and shear modulus. As shown
thermodynamically by Hill,52 the average of the Voigt and
Reuss bounds provide better estimates of the elastic moduli
of polycrystalline materials. By treating the polycrystalline
materials as aggregates of single crystals with random orien-
tations, the isotropic polycrystalline elastic moduli can be
computed as averages of anisotropic single-crystal elastic
constants. The theoretical lower and upper bounds to the true
polycrystalline bulk modulus B and shear modulus G are
given by Reuss (assuming uniform stress throughout a poly-
UDDIN et al.
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Uddin, Jamal; Baskes, Michael I.; Srivilliputhur, Srinivasan; Cundari, Thomas R., 1964- & Wilson, Angela K. Modified embedded atom method study of the mechanical properties of carbon nanotube reinforced nickel composites, article, March 11, 2010; [College Park, Maryland]. (digital.library.unt.edu/ark:/67531/metadc107769/m1/6/: accessed July 28, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.