Modified embedded atom method study of the mechanical properties of carbon nanotube reinforced nickel composites Page: 9
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MODIFIED EMBEDDED ATOM METHOD STUDY OF THE...
TABLE VI. The shear anisotropic factors A1, A2, A3, and AG (in %), AB (in %) for pure Nickel (fcc) and nickel/CNT composites with low
and high CNT volume fractions.
Ni(fcc) A1 (2.516) A2 (2.516) A3 (2.516) AB (0.00) AG (9.875) ABb (1) AB (1)
Low High Low High Low High Low High Low High Low High Low High
Ni/SWCNT(5,0) 2.452 2.155 2.485 2.409 2.370 2.026 0.005 0.047 9.237 7.542 1.056 1.162 1.040 1.148
Ni/SWCNT(10,0) 2.247 1.630 2.504 2.452 2.309 1.838 0.015 0.180 8.602 6.158 1.087 1.305 1.088 1.314
Ni/SWCNT(15,0) 2.113 1.269 2.525 2.539 2.228 1.657 0.020 0.209 8.145 5.874 1.101 1.315 1.098 1.311
Ni/MWCNT 2.002 1.304 2.444 2.181 2.000 1.254 0.102 0.929 7.218 4.985 1.237 1.768 1.223 1.692
From the anisotropy of the directional linear bulk modu-
lus it is clear that fcc nickel does not show any directionality.
However, due to the alignment of the CNTs, the nanocom-
posites show differences in the bulk moduli along different
axes. For example, along the direction of CNT alignment
(i.e., a axis), there is an increase in the bulk modulus
whereas in the transverse directions (i.e., b and c axes) de-
creases are seen compared to Ni. These changes are more
prominent at higher CNT concentrations. These results imply
that the composites are less compressible along the direction
of the CNT axis and more compressible along the transverse
directions. The anisotropy of the bulk modulus ABb and ABc
along the a axis with respect to b and c axes shows that
anisotropy increase with the increasing CNT diameter and
CNT volume fraction. For Ni, the bulk anisotropy (AB) is
zero indicating no anisotropic compressibility. For compos-
ites, AB increases with increase in the CNT volume fraction
and CNT diameters indicating an increase in compressibility.
The maximum value for AB is seen for the Ni/MWCNT com-
AG gives the relative magnitude of the actual elastic an-
isotropy possessed by a crystal.56 In the case of shear aniso-
tropy (AG), MEAM Ni shows the maximum value of 9.88
while a value of 9.76 is reported in the literature.56 This
suggests that Ni has large shear anisotropy. A decrease is
seen for composites with larger CNT radii and volume frac-
tions. Thus, it can be concluded that the composites are also
elastically anisotropic. However, there are significant effects
of CNTs within the composites, the AG decrease and larger
decreases are seen for composites with higher CNT volume
It is interesting to note that the composites have the high-
est directional bulk modulus along the direction in which the
nanotubes are aligned. In the transverse directions, the values
are comparable. This indicates that the compressibility is
smallest along the longitudinal direction and largest along
the transverse direction. Along the CNT alignment direction,
the bulk modulus increases compared to pure nickel and it
decreases in the transverse directions. CNT concentration
also affects the bulk modulus significantly.
4. Interfacial characteristics
We have closely monitored the motion of nickel and car-
bon atoms in Ni/SWCNT(10,0) with low CNT volume frac-
tion at 0.0% and 0.2% applied strains. We find both nickel
and carbon atoms move in concert with each other in the
direction of applied strain. There is little or no movement of
atoms in the transverse directions, except for a few atoms in
the central portion of the cell where Ni atoms are found to
perturb laterally in the perpendicular directions. In the vicin-
ity of the nanotube, it is seen that first few Ni atoms move
away and others shift toward the center during minimization
in this region. The overall relative shifts of atomic positions
during the loading can be quantitatively estimated using the
root mean-square deviations (RMSDs) of the atoms in the
simulation cell from those two strain limits. It is seen that the
RMSD for Ni/CNT system is 0.0214 A in the longitudinal
direction, which interestingly, is virtually identical to the
RMSDs calculated for CNT and Ni atoms separately. Note
that these RMSD calculations were performed by taking on
the central portion of the original cells but reducing it by 1
X 2 X in x, y, and z directions. In the transverse directions,
the RMSD is 0.0007 A, indicating very small or no relative
movement due to applied strain. These results suggest that
both carbon and nickel atom move in concert during uniaxial
loading in the longitudinal direction, without sliding of C
atoms relative to the nickel atoms. This is possible in the
case of a relatively strong Ni/CNT interface. This finding is
also supported by our analysis of rule-of-mixture (RoM) re-
sults, discussed in the next section.
5. Analysis of rule-of-mixture
The properties of fiber-reinforced composites have been
extensively studied to predict their elastic properties.57 One
such approach is the RoM.58,59 For a CNT-reinforced nano-
composites, under uniaxial loading, the dependence of the
Young's modulus on the CNT volume fraction can be theo-
retically estimated as
EC= VfEf+ (1 - V)Em,
where EC is the predicted Young's modulus of the composite,
Ef is the Young's modulus of the fiber reinforcement (CNT),
Em the Young's modulus of the matrix, and VI is the volume
fraction of the CNTs.
We have estimated the Young's modulus in the longitudi-
nal direction (E11) for all Ni/CNT composites and compared
them with the results obtained directly from simulation. Fig-
ure 5 shows Ell as a function of Vf for Ni/CNT composites
(here the full lines plots of the standard RoM expression). It
is clear that the RoMs fit with the simulated results well and
PHYSICAL REVIEW B 81, 104103 (2010)
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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/m1/9/: accessed December 16, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.