Modified embedded atom method study of the mechanical properties of carbon nanotube reinforced nickel composites Page: 5
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MODIFIED EMBEDDED ATOM METHOD STUDY OF THE...
TABLE III. Single-crystal elastic constants cij (in GPa), and derived quantities Cl1+C22-2c12, c22+C33-2c23, c11+C33-2c13, and cll
+c22+c33+2c12+2c23+2c13 for pure fcc nickel and the Ni/SWCNTs and Ni/MWCNT composites with low and high CNT volume fractions.
Ni(fcc) Ni/SWCNT(5,0) Ni/SWCNT(10,0) Ni/SWCNT(15,0) Ni/MWCNT
Low High Low High Low High Low High
c11 247.1 251.9 266.1 256.7 284.0 258.8 289.4 276.9 356.1
c22 247.1 246.0 243.6 245.4 241.5 243.2 233.4 245.7 243.9
c33 247.1 246.0 243.9 245.2 240.6 243.4 233.6 246.3 247.5
c12 147.5 146.6 144.0 145.5 139.7 142.7 129.7 142.9 132.8
c23 147.5 148.3 150.5 147.9 148.8 147.7 147.5 149.1 149.6
c13 147.5 148.0 144.9 145.5 140.1 142.7 129.5 143.6 133.8
c44 125.4 123.7 118.6 118.5 99.6 114.5 83.8 118.2 109.5
c55 125.4 121.4 112.3 121.9 113.1 120.7 109.1 118.4 104.7
c66 125.4 121.4 112.3 121.9 113.1 120.7 109.1 118.4 104.8
Cl1+C22-2c12 199.3 204.7 221.7 211.1 246.1 216.6 263.8 236.8 334.3
C22+ 33-2c23 199.3 201.3 220.1 210.9 244.4 216.8 263.6 236.1 294.9
c11+C33-2c13 199.3 195.5 186.5 194.8 184.5 191.2 172.0 193.8 184.5
c11+c22+c33+2c12+2c23+2c13 1626.2 1630.3 1632.5 1625.1 1623.3 1611.6 1569.8 1640.0 1728.7
In the composites with SWCNTs, c12 and c13 decrease for
both low and high CNT concentrations, which depend on the
CNT diameters and the CNT volume fractions. A larger de-
crease is seen for composites with larger CNT diameters. For
example, in the case of Ni/SWCNT(15,0) with high CNT
volume fraction, the value for C12 and c13 is found to be 18
GPa less than that of Ni. The c23 on the other hand, remain
similar to that of Ni, with a few exceptions, where a minute
increase is seen. For the composites with the MWCNT, c12
and c13 decrease for both low and high CNT volume frac-
tions. For c23, however, a small increase is seen for both
volume fractions. The values of c44, c55, and c66 decrease in
the composites compared to pure Ni (125 GPa) and depend
on the CNT concentration in the composites. A similar trend
is seen for c55 and c66, although these show less variation
than c44. The Ni/MWCNT composites also show similar
CNT concentration dependence for these elastic parameters,
however, the decrease in c44 is less in a relative sense. Note
that c44, C55, and c66 are equivalent to the shear modulus (G).
To study the angular anisotropy of the elastic constants in
Ni/CNT, we performed calculations in which the CNT is
rotated about its tubular axis. Elastic constants from these
calculations are similar to the original unrotated systems.
While lack of anisotropy merits further investigation, the oc-
currence of a regular interfacial structural pattern seems un-
likely because this interface forms between the large periph-
eral surface of the CNT that runs through the entire 7.4 nm
length of the unit cell and the irregular curvature of the Ni
matrix in the perpendicular directions.
The Young's modulus (E) along the normal direction of
the lattice plane is defined as the ratio of the stress to the
strain along that direction. Ell (Eoo0), E22 (Eloo), and E33
(Eolo) were calculated for cubic and orthorhombic lattices
along the principal (a, b, and c) axes. Poisson's ratio v(n, m)
of an elastic solid for any two specified general orthogonal
unit vectors n and m is defined as -e(m)/e(n), where e(m) is
the transverse strain in the direction m and e(n) is the axial
strain in the direction n due to a uniaxial tension of the
material along the direction n. With the exception of isotro-
pic elastic materials, Poisson's ratio for an anisotropic elastic
material depends on the choice of n and m and was calcu-
lated from the elastic compliance values.
Figure 3 presents the calculated values of Ez1, E22, and
E33 for Ni and Ni/CNT composites for two different CNT
volume fractions. For pure Ni, we calculated E of 136.9 GPa
along the major directions. This agrees reasonably well with
an experimental value of 120 GPa.49 For composites, in the
oLo ... E,(E,,)
275L H E010100(E 33)
S \\ C C, ... Emm o (E22 .3)
250 CL L CH ... Epolycrystalline
0 225 -- - - - -
. 2 0 0 ...... ...
-n 175 -......
FIG. 3. (Color online) Calculated Young's modulus (GPa) for
fcc Ni and Ni/CNT composites with two different CNT fractions.
The E001 (E11) is the Young's modulus for uniaxial loading parallel
to CNT axis, the Eoo010 (E22) or E100 (E33) are the Young's moduli in
the directions transverse to the CNT axis in single-crystal systems,
and Epolycrystalline is the Young's modulus for polycrystalline aggre-
gates. Composites with low CNT fractions are designated as CL and
composites with high CNT fractions are designated as CL.
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/m1/5/: accessed November 25, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.