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Modelling Mechanical and Thermal Properties of Carbon Nanotubes Reinforced Metal Matrix Composites

Profile image of Gehad HamdanGehad Hamdan

2017

Abstract

the chairman of my supervisory committee, for his excellent supervision, constructive comments. My thanks also goes to the members of my supervisory committee, Dr. Al-Khawad Ali Elfaki for his ennobling association, and for giving me another dimension to life and taking time off from his busy schedule to serve in the committee. My thanks also go to Dr.

Figures (425)
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nanometer size diameter as shown in Figure 2.2 layer of crystalline graphite, called a graphene sheet, seamlessly rolled into a cylinder of
nanometer size diameter as shown in Figure 2.2 layer of crystalline graphite, called a graphene sheet, seamlessly rolled into a cylinder of
Figure 2.1: The allotropic forms of carbon known to mankind
Figure 2.1: The allotropic forms of carbon known to mankind
Table 2.1: Parameters of carbon nanotubes[41]
Table 2.1: Parameters of carbon nanotubes[41]
Table 2.2: Overview on the most common carbon nanotubes synthesis techniques and their advantages and disadvantages.[46]
Table 2.2: Overview on the most common carbon nanotubes synthesis techniques and their advantages and disadvantages.[46]
doubt that their unique properties will lead to better and newer materials.
doubt that their unique properties will lead to better and newer materials.
Table 2.5: Thermal properties of Carbon nanotubes[49]
Table 2.5: Thermal properties of Carbon nanotubes[49]
Figure 2.7: The various processes for synthesis of CNT-reinforced composite[52]
Figure 2.7: The various processes for synthesis of CNT-reinforced composite[52]
fractions are: Ultimate fiber arrays for (a): square, (b) hexagonal, and (c) layer- wise fiber distributions.[74] rays are presented in Figure 2.10, and the corresponding ultimate fiber volum«
fractions are: Ultimate fiber arrays for (a): square, (b) hexagonal, and (c) layer- wise fiber distributions.[74] rays are presented in Figure 2.10, and the corresponding ultimate fiber volum«
is isotropic in the 2-3 plane. Figure 2.11: Schematic representation of unidirectional composite [74] unidirectional composite or ply can be considered to be transversely isotropic; that is, it
is isotropic in the 2-3 plane. Figure 2.11: Schematic representation of unidirectional composite [74] unidirectional composite or ply can be considered to be transversely isotropic; that is, it
Figure 2.12: Response of various types of materials under uniaxial normal and pure shear loading [72] The basic assumptions dealing with fiber- matrix interactions in a unidirectional lamina
Figure 2.12: Response of various types of materials under uniaxial normal and pure shear loading [72] The basic assumptions dealing with fiber- matrix interactions in a unidirectional lamina
Figure 2.13: Representative Volume Element Loaded along the fiber direction applied on the composite lamina is shared by the fibers and the matrix so that: that the fiber stress of is always greater than the matrix stress 0,,. The tensile force P, Comparing Equation 2.15 with Equation 2.16 and noting that Ey > E,,, we conclude The loads P. , P; , and P, carried by the composite, the fibers, and the matrix, respectively, may be written as follows in terms of stresses O¢ , O¢ , and Oy; experienced
Figure 2.13: Representative Volume Element Loaded along the fiber direction applied on the composite lamina is shared by the fibers and the matrix so that: that the fiber stress of is always greater than the matrix stress 0,,. The tensile force P, Comparing Equation 2.15 with Equation 2.16 and noting that Ey > E,,, we conclude The loads P. , P; , and P, carried by the composite, the fibers, and the matrix, respectively, may be written as follows in terms of stresses O¢ , O¢ , and Oy; experienced
considered to be made up of layers representing fibers and matrix material as shown in
considered to be made up of layers representing fibers and matrix material as shown in
Figure 2.15: Shear loading and deformation of a Representative Volume Element deformations are shown in Figure 2.15. The total shearing deformation is defined in
Figure 2.15: Shear loading and deformation of a Representative Volume Element deformations are shown in Figure 2.15. The total shearing deformation is defined in
Figure 2.16: Shear deformation of a Representative Volume Element the deformation pattern for cumulative thickness of layers. load parallel to the fibers, that is, parallel to the layers in the model. Figure 2.16 shows
Figure 2.16: Shear deformation of a Representative Volume Element the deformation pattern for cumulative thickness of layers. load parallel to the fibers, that is, parallel to the layers in the model. Figure 2.16 shows
Figure 2.17: Longitudinal tensile loading of a unidirectional discontinuous fiber lamina. simple force equilibrium analysis as shown in Figure 2.17 fibers, we can calculate the normal stress distribution in a discontinuous fiber by a stress transfer at the fiber end cross sections and the interaction between the neighboring
Figure 2.17: Longitudinal tensile loading of a unidirectional discontinuous fiber lamina. simple force equilibrium analysis as shown in Figure 2.17 fibers, we can calculate the normal stress distribution in a discontinuous fiber by a stress transfer at the fiber end cross sections and the interaction between the neighboring
Figure 2.18: Definition of principal material axes and loading axes for a lamina represent the loading directions.[70, 71]
Figure 2.18: Definition of principal material axes and loading axes for a lamina represent the loading directions.[70, 71]
these types of materials, these differences are demonstrated schematically in Figure 2.19 orthotropic, and anisotropic materials are also reflected in the mechanics and design of
these types of materials, these differences are demonstrated schematically in Figure 2.19 orthotropic, and anisotropic materials are also reflected in the mechanics and design of
):; Applications of (a) longitudinal tensile stress, (b) transverse tensile stress, and (c) in-plane shear stress on a unidirectional continuous fiber 0° lamina [70] from the following equations: Elastic properties of a unidirectional continuous fiber 0° lamina, are calculated 2.6.4.1 Unidirectional Continuous Fiber 0° Lamina
):; Applications of (a) longitudinal tensile stress, (b) transverse tensile stress, and (c) in-plane shear stress on a unidirectional continuous fiber 0° lamina [70] from the following equations: Elastic properties of a unidirectional continuous fiber 0° lamina, are calculated 2.6.4.1 Unidirectional Continuous Fiber 0° Lamina
Where Ey, , Eno, 912 , and Gy, are calculated using Equations 2.60 through 2.64.[70] with the positive x direction.
Where Ey, , Eno, 912 , and Gy, are calculated using Equations 2.60 through 2.64.[70] with the positive x direction.
tensor, 04, as shown in Figure 2.21. Correspondingly, there is a strain tensor, €j , will Figure 2.21: The six components to describe the state of stress at a point. Generally, the state of stress at a point is described by the nine components of the stress
tensor, 04, as shown in Figure 2.21. Correspondingly, there is a strain tensor, €j , will Figure 2.21: The six components to describe the state of stress at a point. Generally, the state of stress at a point is described by the nine components of the stress
stress—strain relationships at a point in an x—y—z orthogonal system in matrix form are: Where, 9 is the Poisson’s ratio. The shear modulus G is a function of two elastic For a linear isotropic material in a three-dimensional stress state, the Hooke’s lav
stress—strain relationships at a point in an x—y—z orthogonal system in matrix form are: Where, 9 is the Poisson’s ratio. The shear modulus G is a function of two elastic For a linear isotropic material in a three-dimensional stress state, the Hooke’s lav
The [S] matrix is the compliance matrix for the especially orthotropic lamina. Inverting fiber can be written as: [70-72, 75, and 78] such as unidirectional fiber reinforced composite loaded parallel or perpendicular to th lamina as: [70-72, 75, and 78] From Hook’s law, strain-stress relation for linear elastically orthotropic material,
The [S] matrix is the compliance matrix for the especially orthotropic lamina. Inverting fiber can be written as: [70-72, 75, and 78] such as unidirectional fiber reinforced composite loaded parallel or perpendicular to th lamina as: [70-72, 75, and 78] From Hook’s law, strain-stress relation for linear elastically orthotropic material,
Similarly, the strain transformation equations are: [70-72, 75, and 78] Figure 2.23: Positive Rotation of Principal Material Axis from XY Axis Where, @ is the angle from the x-axis to the 1-axis as shown in Figure 2.23 The stress-strain relations for a general orthotropic lamina, Equations 2.76 can be
Similarly, the strain transformation equations are: [70-72, 75, and 78] Figure 2.23: Positive Rotation of Principal Material Axis from XY Axis Where, @ is the angle from the x-axis to the 1-axis as shown in Figure 2.23 The stress-strain relations for a general orthotropic lamina, Equations 2.76 can be
ire 2.24: Development of a continuum model for a SWNT. a) Schematic diagram of a carbon nanotube; b) Equivalent continuum model; c) Effective solid fiber; and d) a prolate spheroidal inclusion. [89] By using the definition of heat flux,
ire 2.24: Development of a continuum model for a SWNT. a) Schematic diagram of a carbon nanotube; b) Equivalent continuum model; c) Effective solid fiber; and d) a prolate spheroidal inclusion. [89] By using the definition of heat flux,
Figure 2.25: Different material modeling techniques[94]
Figure 2.25: Different material modeling techniques[94]
gure 2.26: Equivalence of molecular mechanics and structural mechanics for covalent and non-covalent interactions between carbon atoms: (a) Molecular mechanics model and (b) structural mechanics model.[8, 113, 114] elements and the molecular forces between bonded carbon atoms.
gure 2.26: Equivalence of molecular mechanics and structural mechanics for covalent and non-covalent interactions between carbon atoms: (a) Molecular mechanics model and (b) structural mechanics model.[8, 113, 114] elements and the molecular forces between bonded carbon atoms.
To determine the force constants pertaining to the covalent interactions one could equate the potential energies of individual bonds with their corresponding beam
To determine the force constants pertaining to the covalent interactions one could equate the potential energies of individual bonds with their corresponding beam
The volume fraction of the carbon nanotube is given by:
The volume fraction of the carbon nanotube is given by:
Figure 3.5: Flow chart describes the MATLAB program used for calculation of Thermal conductivity process of the calculation of thermal conductivity is presented in Figure 3.5
Figure 3.5: Flow chart describes the MATLAB program used for calculation of Thermal conductivity process of the calculation of thermal conductivity is presented in Figure 3.5
Figure 3.6: Steps involved for finite element method
Figure 3.6: Steps involved for finite element method
Figure 3.7: Two possible RVEs for the analysis of CNT-based Nanocomposite (a) Square RVE with long fiber; (b) Square RVE with short fiber representative volume element assumed to be 10 nm.
Figure 3.7: Two possible RVEs for the analysis of CNT-based Nanocomposite (a) Square RVE with long fiber; (b) Square RVE with short fiber representative volume element assumed to be 10 nm.
Table 3.1: Model dimensions for long carbon nanotubes case
Table 3.1: Model dimensions for long carbon nanotubes case
represents the geometry of the PLANE 182 element.
represents the geometry of the PLANE 182 element.
such as B-bar, uniformly reduced integration, and enhanced strains are supported. Figure 3.11: SOLID185 Homogeneous Structural Solid Geometry[138] pyramid degenerations when used in irregular regions. Various element technologies
such as B-bar, uniformly reduced integration, and enhanced strains are supported. Figure 3.11: SOLID185 Homogeneous Structural Solid Geometry[138] pyramid degenerations when used in irregular regions. Various element technologies
Figure 3.12: FE mesh for the RVE 3.12 and 3.13 show the meshing procedure for quarter and full model.
Figure 3.12: FE mesh for the RVE 3.12 and 3.13 show the meshing procedure for quarter and full model.
Figure 3.13: The mesh of Full model
Figure 3.13: The mesh of Full model
Figure 3.15: The periodic condition in x direction For preventing rigid motion, any one node inside representative volume element is fully For periodic boundary condition in x direction Continue the formulation by consider the detailed boundary condition for 3D problem.
Figure 3.15: The periodic condition in x direction For preventing rigid motion, any one node inside representative volume element is fully For periodic boundary condition in x direction Continue the formulation by consider the detailed boundary condition for 3D problem.
For periodic boundary condition in z direction For periodic boundary condition in y direction
For periodic boundary condition in z direction For periodic boundary condition in y direction
In other hand, the constitutive relationship is as follows Combining equation 3.11 and 3.12, stiffness matrix [c| is evaluated and inverted —1 stiffness matrix [C]" is computed. For the transverse isotropic material,
In other hand, the constitutive relationship is as follows Combining equation 3.11 and 3.12, stiffness matrix [c| is evaluated and inverted —1 stiffness matrix [C]" is computed. For the transverse isotropic material,
In this thesis, simulations will be conducted with ANSYS software using square
In this thesis, simulations will be conducted with ANSYS software using square
Figure 4.1: Density for carbon nanotube reinforced iron, copper and aluminum
Figure 4.1: Density for carbon nanotube reinforced iron, copper and aluminum
Figure 4.2: Effect of volume fraction on longitudinal Young’s modulus for carbon nanotube treated as long fiber reinforced iron, copper and aluminum metal matrix carbon nanotubes increased from 3%, 7%, and 11%.
Figure 4.2: Effect of volume fraction on longitudinal Young’s modulus for carbon nanotube treated as long fiber reinforced iron, copper and aluminum metal matrix carbon nanotubes increased from 3%, 7%, and 11%.
gure 4.3: Effect of volume fraction on transverse modulus for carbon nanotube treated as long fiber reinforced iron, copper and aluminum metal matrix
gure 4.3: Effect of volume fraction on transverse modulus for carbon nanotube treated as long fiber reinforced iron, copper and aluminum metal matrix
4: Effect of volume fraction on shear modulus for carbon nanotube treated as long fiber reinforced iron, copper and aluminum metal matrix
4: Effect of volume fraction on shear modulus for carbon nanotube treated as long fiber reinforced iron, copper and aluminum metal matrix
Effect of volume fraction on major Poisson's ratio for carbon nanotube treated as long fiber reinforced iron, copper and aluminum metal matrix reinforcement have the same Poisson’s ratio value.
Effect of volume fraction on major Poisson's ratio for carbon nanotube treated as long fiber reinforced iron, copper and aluminum metal matrix reinforcement have the same Poisson’s ratio value.
e 4.9: Longitudinal Young's modulus for zigzag (5,0) carbon nanotube (different length) reinforced copper metal matrix volume fraction increases.
e 4.9: Longitudinal Young's modulus for zigzag (5,0) carbon nanotube (different length) reinforced copper metal matrix volume fraction increases.
ure 4.10: Longitudinal Young's modulus for armchair (5,5) carbon nanotube (different length) reinforced copper metal matrix
ure 4.10: Longitudinal Young's modulus for armchair (5,5) carbon nanotube (different length) reinforced copper metal matrix
Figure 4.11: Longitudinal Young's modulus for chiral (5,10) carbon nanotube (different length) reinforced copper metal matrix For carbon nanotube reinforced aluminum matrix Nanocomposite, It was observed
Figure 4.11: Longitudinal Young's modulus for chiral (5,10) carbon nanotube (different length) reinforced copper metal matrix For carbon nanotube reinforced aluminum matrix Nanocomposite, It was observed
Longitudinal Young's modulus for zigzag (5,0)carbon nanotube (different length) reinforced aluminum metal matrix respectively when the volume fraction increases.
Longitudinal Young's modulus for zigzag (5,0)carbon nanotube (different length) reinforced aluminum metal matrix respectively when the volume fraction increases.
Figure 4.13: Longitudinal Young's modulus for armchair (5,5) carbon nanotube (different length) reinforced aluminum metal matrix
Figure 4.13: Longitudinal Young's modulus for armchair (5,5) carbon nanotube (different length) reinforced aluminum metal matrix
Longitudinal Young's modulus for chiral (5,10) carbon nanotube (different length) reinforced aluminum metal matrix
Longitudinal Young's modulus for chiral (5,10) carbon nanotube (different length) reinforced aluminum metal matrix
Effect of armchair carbon nanotube diameter on Young’s modulus for reinforced: (a) iron, (b) copper, and (c) aluminum matrix Similarly, the prediction of Young’s modulus for the copper and aluminum matrix
Effect of armchair carbon nanotube diameter on Young’s modulus for reinforced: (a) iron, (b) copper, and (c) aluminum matrix Similarly, the prediction of Young’s modulus for the copper and aluminum matrix
of the armchair carbon nanotubes increases. For zigzag carbon nanotubes reinforced iron metal matrix at same length with different copper and aluminum matrix, the value of Young’s modulus decreases as the diameter
of the armchair carbon nanotubes increases. For zigzag carbon nanotubes reinforced iron metal matrix at same length with different copper and aluminum matrix, the value of Young’s modulus decreases as the diameter
Similarly, the prediction of Young’s modulus for the copper and aluminum matrix Effect of chiral carbon nanotube diameter on Young’s modulus for reinforced: (a) iron, (b) copper, and (c) aluminum matrix and (c). It can be observed that at 3% volume fraction of carbon nanotube reinforced of Young’s modulus decreases as the diameter of the chiral carbon nanotubes increases.
Similarly, the prediction of Young’s modulus for the copper and aluminum matrix Effect of chiral carbon nanotube diameter on Young’s modulus for reinforced: (a) iron, (b) copper, and (c) aluminum matrix and (c). It can be observed that at 3% volume fraction of carbon nanotube reinforced of Young’s modulus decreases as the diameter of the chiral carbon nanotubes increases.
ible 4.4: Effect of chiral index on the Young’s modulus of iron matrix (V;=3%) Similarly the procedure will be taken for the prediction of Young’s modulus for the
ible 4.4: Effect of chiral index on the Young’s modulus of iron matrix (V;=3%) Similarly the procedure will be taken for the prediction of Young’s modulus for the
Longitudinal Young's modulus for different chiral index carbon nanotube (at length Ic=3 nm) reinforced iron metal matrix
Longitudinal Young's modulus for different chiral index carbon nanotube (at length Ic=3 nm) reinforced iron metal matrix
Longitudinal Young's modulus for different chiral index carbon nanotube (at length Ic=5 nm) reinforced iron metal matrix
Longitudinal Young's modulus for different chiral index carbon nanotube (at length Ic=5 nm) reinforced iron metal matrix
ible 4.5: Effect of chiral index on the Young’s modulus of copper matrix (Vf=3%)
ible 4.5: Effect of chiral index on the Young’s modulus of copper matrix (Vf=3%)
; Longitudinal Young's modulus for different chiral index carbon nanotube (at length lc=5 nm) reinforced copper metal matrix
; Longitudinal Young's modulus for different chiral index carbon nanotube (at length lc=5 nm) reinforced copper metal matrix
1.20: Longitudinal Young's modulus for different chiral index carbon nanotube (at length lc=8 nm) reinforced copper metal matrix
1.20: Longitudinal Young's modulus for different chiral index carbon nanotube (at length lc=8 nm) reinforced copper metal matrix
figure 4.21: Longitudinal Young's modulus for different chiral index carbon nanotube (at length lc=3nm) reinforced aluminum metal matrix
figure 4.21: Longitudinal Young's modulus for different chiral index carbon nanotube (at length lc=3nm) reinforced aluminum metal matrix
le 4.8: Transverse modulus prediction for (a) armchair, (b) zigzag, and (c) chiral carbon nanotubes reinforced copper metal matrix A wimohair
le 4.8: Transverse modulus prediction for (a) armchair, (b) zigzag, and (c) chiral carbon nanotubes reinforced copper metal matrix A wimohair
‘igure 4.24; Transverse Young's modulus for carbon nanotube as short fiber reinforced iron metal matrix
‘igure 4.24; Transverse Young's modulus for carbon nanotube as short fiber reinforced iron metal matrix
Figure 4.25: Transverse Young's modulus for carbon nanotube as short fiber reinforced copper metal matrix
Figure 4.25: Transverse Young's modulus for carbon nanotube as short fiber reinforced copper metal matrix
‘igure 4.26: Transverse Young's modulus for carbon nanotube as short fibe reinforced aluminum metal matrix
‘igure 4.26: Transverse Young's modulus for carbon nanotube as short fibe reinforced aluminum metal matrix
Figure 4.27: Shear modulus for carbon nanotube (as short fiber) reinforced iron matrix depends on the ratio between the values of fiber to matrix shear modulus.
Figure 4.27: Shear modulus for carbon nanotube (as short fiber) reinforced iron matrix depends on the ratio between the values of fiber to matrix shear modulus.
The parameters Cy and c can be obtained from equation 2.94 and 2.98 by using
The parameters Cy and c can be obtained from equation 2.94 and 2.98 by using
Figures 4.30, 4.31, and 4.32 show the effect of volume fraction on the thermal
Figures 4.30, 4.31, and 4.32 show the effect of volume fraction on the thermal
4.13: Comparison between different carbon nanotube chiral index on the thermal conductivity for reinforcing aluminum metal matrix (Vi=3%)
4.13: Comparison between different carbon nanotube chiral index on the thermal conductivity for reinforcing aluminum metal matrix (Vi=3%)
has the lowest slope.
has the lowest slope.
Figure 4.31: Effect of volume fraction on thermal conductivity for zigzag carbon nanotube reinforced aluminum metal matrix
Figure 4.31: Effect of volume fraction on thermal conductivity for zigzag carbon nanotube reinforced aluminum metal matrix
‘igure 4.32: Effect of volume fraction on thermal conductivity for chiral carbor reinforced aluminum metal matrix
‘igure 4.32: Effect of volume fraction on thermal conductivity for chiral carbor reinforced aluminum metal matrix
Figure 4.33: Effect of volume fraction on thermal conductivity for different chiral indices carbon nanotube reinforced aluminum metal matrix
Figure 4.33: Effect of volume fraction on thermal conductivity for different chiral indices carbon nanotube reinforced aluminum metal matrix
i4: Effect of carbon nanotube chiral index on the thermal conductivity for reinforcing copper metal matrix (Vf=3%) Figure 4.34, 4.35, and 4.36 show the effect of volume fraction on the thermal
i4: Effect of carbon nanotube chiral index on the thermal conductivity for reinforcing copper metal matrix (Vf=3%) Figure 4.34, 4.35, and 4.36 show the effect of volume fraction on the thermal
Figure 4.37 represents the effect of chiral index of carbon nanotubes on the thermal
Figure 4.37 represents the effect of chiral index of carbon nanotubes on the thermal
Figure 4.34: Effect of volume fraction on thermal conductivity for armchair carbon nanotube reinforced copper metal matrix type has the lowest slope.
Figure 4.34: Effect of volume fraction on thermal conductivity for armchair carbon nanotube reinforced copper metal matrix type has the lowest slope.
figure 4.36: Effect of volume fraction on thermal conductivity for chiral carbon nanotube reinforced copper metal matrix
figure 4.36: Effect of volume fraction on thermal conductivity for chiral carbon nanotube reinforced copper metal matrix
ile 4.17; Comparison between different carbon nanotube chiral index on the thermal conductivity for reinforcing iron metal matrix (Vf=3%)
ile 4.17; Comparison between different carbon nanotube chiral index on the thermal conductivity for reinforcing iron metal matrix (Vf=3%)
Figure 4.38: Effect of volume fraction on thermal conductivity for armchair carbon nanotube reinforced iron metal matrix varies linearly with the change in volume fractions as predicted by theoretical model. respectively. It can be observed that the thermal conductivity of the nanocomposite
Figure 4.38: Effect of volume fraction on thermal conductivity for armchair carbon nanotube reinforced iron metal matrix varies linearly with the change in volume fractions as predicted by theoretical model. respectively. It can be observed that the thermal conductivity of the nanocomposite
‘igure 4.39: Effect of volume fraction on thermal conductivity for zigzag carbon nanotube reinforced iron metal matrix
‘igure 4.39: Effect of volume fraction on thermal conductivity for zigzag carbon nanotube reinforced iron metal matrix
Figure 4.41: Effect of volume fraction on thermal conductivity for different chiral index carbon nanotube reinforced iron metal matrix
Figure 4.41: Effect of volume fraction on thermal conductivity for different chiral index carbon nanotube reinforced iron metal matrix
Figure 4.43: Effect of length on thermal conductivity for zigzag carbon nanotube reinforced aluminum metal matrix
Figure 4.43: Effect of length on thermal conductivity for zigzag carbon nanotube reinforced aluminum metal matrix
Figure 4.44; Effect of length on thermal conductivity for chiral carbon nanotube reinforced aluminum metal matrix
Figure 4.44; Effect of length on thermal conductivity for chiral carbon nanotube reinforced aluminum metal matrix
Figure 4.46: Effect of length on thermal conductivity for armchair carbon nanotube reinforced copper metal matrix carbon nanotubes reinforced copper metal matrix.
Figure 4.46: Effect of length on thermal conductivity for armchair carbon nanotube reinforced copper metal matrix carbon nanotubes reinforced copper metal matrix.
Figure 4.47: Effect of length on thermal conductivity for zigzag carbon nanotube reinforced copper metal matrix
Figure 4.47: Effect of length on thermal conductivity for zigzag carbon nanotube reinforced copper metal matrix
Figure 4.49; Effect of length on thermal conductivity for different chiral indice: carbon nanotube reinforced copper metal matrix
Figure 4.49; Effect of length on thermal conductivity for different chiral indice: carbon nanotube reinforced copper metal matrix
Figure 4.50: Effect of length on thermal conductivity for armchair carbon reinforced iron metal matrix
Figure 4.50: Effect of length on thermal conductivity for armchair carbon reinforced iron metal matrix
Figure 4.52: Effect of length on thermal conductivity for chiral carbon reinforced iron metal matrix
Figure 4.52: Effect of length on thermal conductivity for chiral carbon reinforced iron metal matrix
Figure 4.53: Effect of length on thermal conductivity for different chiral indices carbon nanotube reinforced iron metal matrix
Figure 4.53: Effect of length on thermal conductivity for different chiral indices carbon nanotube reinforced iron metal matrix
However, for chiral carbon nanotube, Table 4.20 represents the results of thermal
However, for chiral carbon nanotube, Table 4.20 represents the results of thermal
Figure 4.54; Effect of diameter on thermal conductivity for armchair carbon nanotube reinforced iron metal matrix
Figure 4.54; Effect of diameter on thermal conductivity for armchair carbon nanotube reinforced iron metal matrix
le 4.20: Effect of chiral carbon nanotube diameter on the thermal conductivity for reinforcing iron matrix (V=3%) figure 4.56: Effect of diameter on thermal conductivity for chiral carbon nanotube reinforced iron metal matrix
le 4.20: Effect of chiral carbon nanotube diameter on the thermal conductivity for reinforcing iron matrix (V=3%) figure 4.56: Effect of diameter on thermal conductivity for chiral carbon nanotube reinforced iron metal matrix
able 4.21: Effect of armchair carbon nanotube diameter on the thermal conductivity for reinforcing copper matrix (V=3% )
able 4.21: Effect of armchair carbon nanotube diameter on the thermal conductivity for reinforcing copper matrix (V=3% )
Effect of zigzag carbon nanotube diameter on the thermal conductivity for reinforcing copper matrix (V;=3%) Figure 4.58: Effect of diameter on thermal conductivity for zigzag carbon nanotube reinforced copper metal matrix
Effect of zigzag carbon nanotube diameter on the thermal conductivity for reinforcing copper matrix (V;=3%) Figure 4.58: Effect of diameter on thermal conductivity for zigzag carbon nanotube reinforced copper metal matrix
armchair carbon nanotubes types reinforced aluminum matrix Nanocomposite.
armchair carbon nanotubes types reinforced aluminum matrix Nanocomposite.
4.24: Effect of armchair carbon nanotube diameter on the thermal conductivity for reinforcing aluminum matrix (Vj=3% )
4.24: Effect of armchair carbon nanotube diameter on the thermal conductivity for reinforcing aluminum matrix (Vj=3% )
Figure 4.61: Effect of diameter on thermal conductivity for zigzag carbon nanotube reinforced aluminum metal matrix
Figure 4.61: Effect of diameter on thermal conductivity for zigzag carbon nanotube reinforced aluminum metal matrix
aluminum matrix Nanocomposite. From the previous analysis, it can be observed that zigzag (5, 0) type show higher
aluminum matrix Nanocomposite. From the previous analysis, it can be observed that zigzag (5, 0) type show higher
Figure 4.63: Effect of thermal contact conductance on thermal conductivity for armchair carbon nanotube (5, 5) reinforced iron metal matrix of perfect contact between the matrix and carbon nanotubes.
Figure 4.63: Effect of thermal contact conductance on thermal conductivity for armchair carbon nanotube (5, 5) reinforced iron metal matrix of perfect contact between the matrix and carbon nanotubes.
Figure 4.64: Effect of thermal contact conductance on thermal conductivity for zigzag carbon nanotube (5, 0) reinforced iron metal matrix
Figure 4.64: Effect of thermal contact conductance on thermal conductivity for zigzag carbon nanotube (5, 0) reinforced iron metal matrix
Effect of thermal contact conductance on thermal conductivity for different chiral index of reinforced iron matrix at different lengths (Vi=3 % ) The results calculated at 3% volume fraction and length was |, =3 nm show slightly
Effect of thermal contact conductance on thermal conductivity for different chiral index of reinforced iron matrix at different lengths (Vi=3 % ) The results calculated at 3% volume fraction and length was |, =3 nm show slightly
Figure 4.65: Effect of thermal contact conductance on thermal conductivity for chiral carbon nanotube (5, 10) reinforced iron metal matrix
Figure 4.65: Effect of thermal contact conductance on thermal conductivity for chiral carbon nanotube (5, 10) reinforced iron metal matrix
ure 4.66: Effect of thermal contact conductance on thermal conductivity for different chiral Indices carbon nanotube reinforced iron metal matrix (at Ic=3 nm) different lengths.
ure 4.66: Effect of thermal contact conductance on thermal conductivity for different chiral Indices carbon nanotube reinforced iron metal matrix (at Ic=3 nm) different lengths.
igure 4.67: Effect of thermal contact conductance on thermal conductivity for different chiral Indices carbon nanotube reinforced iron metal matrix (at Ic=5 nm)
igure 4.67: Effect of thermal contact conductance on thermal conductivity for different chiral Indices carbon nanotube reinforced iron metal matrix (at Ic=5 nm)
‘igure 4.68: Effect of thermal contact conductance on thermal conductivity for different chiral Indices carbon nanotube reinforced iron metal matrix (at Ilc=8 nm)
‘igure 4.68: Effect of thermal contact conductance on thermal conductivity for different chiral Indices carbon nanotube reinforced iron metal matrix (at Ilc=8 nm)
assumption of perfect contact between the matrix and carbon nanotubes. Figure 4.70: Effect of thermal contact conductance on thermal conductivity for zigzag carbon nanotube (5, 0) reinforced copper metal matrix
assumption of perfect contact between the matrix and carbon nanotubes. Figure 4.70: Effect of thermal contact conductance on thermal conductivity for zigzag carbon nanotube (5, 0) reinforced copper metal matrix
34: Effect of thermal contact conductance on thermal conductivity for chiral carbon nanotube reinforced copper matrix at different length: (a) at 1. =3 nm, (b) at 1. =5 nm, and (c) at 1. =8 nm
34: Effect of thermal contact conductance on thermal conductivity for chiral carbon nanotube reinforced copper matrix at different length: (a) at 1. =3 nm, (b) at 1. =5 nm, and (c) at 1. =8 nm
Figure 4.71: Effect of thermal contact conductance on thermal conductivity for chiral carbon nanotube (5, 10) reinforced copper metal matrix
Figure 4.71: Effect of thermal contact conductance on thermal conductivity for chiral carbon nanotube (5, 10) reinforced copper metal matrix
Figure 4.73: Effect of thermal contact conductance on thermal conductivity for different chiral indices carbon nanotube reinforced copper metal matrix (at Ic=5 nm)
Figure 4.73: Effect of thermal contact conductance on thermal conductivity for different chiral indices carbon nanotube reinforced copper metal matrix (at Ic=5 nm)
igure 4.74; Effect of thermal contact conductance on thermal conductivity for different chiral indices carbon nanotube reinforced copper metal matrix (at Ic=8 nm)
igure 4.74; Effect of thermal contact conductance on thermal conductivity for different chiral indices carbon nanotube reinforced copper metal matrix (at Ic=8 nm)
From the Tables 4.36 (a), (b), and (c), the effect of thermal contact conductance on the
From the Tables 4.36 (a), (b), and (c), the effect of thermal contact conductance on the
Effect of thermal contact conductance on thermal conductivity for zigzag carbon nanotube reinforced aluminum matrix at different length: (a) at 1. =3 nm, (b) at |. =5 nm, and (c) at |. =8 nm
Effect of thermal contact conductance on thermal conductivity for zigzag carbon nanotube reinforced aluminum matrix at different length: (a) at 1. =3 nm, (b) at |. =5 nm, and (c) at |. =8 nm
gure 4.75; Effect of thermal contact conductance on Thermal Conductivity for armchair carbon nanotube (5, 5) (different length) reinforced aluminum metal matrix
gure 4.75; Effect of thermal contact conductance on Thermal Conductivity for armchair carbon nanotube (5, 5) (different length) reinforced aluminum metal matrix
Effect of thermal contact conductance on thermal conductivity for chiral carbon nanotube reinforced aluminum matrix at different length: (a) atl. =3 nm, (b) at |. =5 nm, and (c) at I. =8 nm
Effect of thermal contact conductance on thermal conductivity for chiral carbon nanotube reinforced aluminum matrix at different length: (a) atl. =3 nm, (b) at |. =5 nm, and (c) at I. =8 nm
From the above Tables, for chiral (5, 10) carbon nanotube reinforced aluminum metal
From the above Tables, for chiral (5, 10) carbon nanotube reinforced aluminum metal
gure 4.77: Effect of thermal contact conductance on thermal conductivity for chiral carbon nanotube (5, 10) (different length) reinforced aluminum metal matrix between the matrix and carbon nanotubes.
gure 4.77: Effect of thermal contact conductance on thermal conductivity for chiral carbon nanotube (5, 10) (different length) reinforced aluminum metal matrix between the matrix and carbon nanotubes.
Effect of thermal contact conductance on thermal conductivity for different chiral index of reinforced aluminum matrix at different lengths
Effect of thermal contact conductance on thermal conductivity for different chiral index of reinforced aluminum matrix at different lengths
sure 4.78: Effect of thermal contact conductance on thermal conductivity for different chiral Index carbon nanotube reinforced aluminum metal matrix (at Ic=3 nm)
sure 4.78: Effect of thermal contact conductance on thermal conductivity for different chiral Index carbon nanotube reinforced aluminum metal matrix (at Ic=3 nm)
ure 4.80: Effect of thermal contact conductance on thermal conductivity for different chiral Index carbon nanotube reinforced aluminum metal matrix (at Ilc=8 nm)
ure 4.80: Effect of thermal contact conductance on thermal conductivity for different chiral Index carbon nanotube reinforced aluminum metal matrix (at Ilc=8 nm)
and aluminum matrices.
and aluminum matrices.
is because the values are relatively near each other’s. It can be observed that the results plotted have a linear trend while it’s not in reality this
is because the values are relatively near each other’s. It can be observed that the results plotted have a linear trend while it’s not in reality this
is because the values are relatively near each other’s. It can be observed that the results plotted have a linear trend while it’s not in reality this
is because the values are relatively near each other’s. It can be observed that the results plotted have a linear trend while it’s not in reality this
Major Poisson’s ratio FEA results for (a) iron, (b) copper, and (c) aluminum matrices Figure 5.4 shows the effect of volume fraction on the major Poisson’s ratio the carbon
Major Poisson’s ratio FEA results for (a) iron, (b) copper, and (c) aluminum matrices Figure 5.4 shows the effect of volume fraction on the major Poisson’s ratio the carbon
nanotubes reinforced iron, copper, and aluminum matrices nanocomposite, respectively.
nanotubes reinforced iron, copper, and aluminum matrices nanocomposite, respectively.
when the volume fraction increases. iron matrix reinforced by zigzag, armchair and chiral carbon nanotube, respectively,
when the volume fraction increases. iron matrix reinforced by zigzag, armchair and chiral carbon nanotube, respectively,
igure 5.6: Longitudinal Young's modulus for carbon nanotube (5,5) (different length) reinforced iron metal matrix
igure 5.6: Longitudinal Young's modulus for carbon nanotube (5,5) (different length) reinforced iron metal matrix
igure 5.7: Longitudinal Young's modulus for carbon nanotube (5, 10) (different length) reinforced iron metal matrix
igure 5.7: Longitudinal Young's modulus for carbon nanotube (5, 10) (different length) reinforced iron metal matrix
igure 5.8: Longitudinal Young's modulus for carbon nanotube (5,0) (different length ) reinforced copper metal matrix
igure 5.8: Longitudinal Young's modulus for carbon nanotube (5,0) (different length ) reinforced copper metal matrix
Figure 5.10: Longitudinal Young's modulus for carbon nanotube (5, 10) (different length) reinforced copper metal matrix
Figure 5.10: Longitudinal Young's modulus for carbon nanotube (5, 10) (different length) reinforced copper metal matrix
armchair and chiral carbon nanotube, respectively, when the volume fraction increases.
armchair and chiral carbon nanotube, respectively, when the volume fraction increases.
Figure 5.12: Longitudinal Young's modulus for carbon nanotube (5, 5) (Different Length) reinforced aluminum metal matrix
Figure 5.12: Longitudinal Young's modulus for carbon nanotube (5, 5) (Different Length) reinforced aluminum metal matrix
Figure 5.13: Longitudinal Young's modulus for carbon nanotube (5, 10) (different length) reinforced aluminum metal matrix
Figure 5.13: Longitudinal Young's modulus for carbon nanotube (5, 10) (different length) reinforced aluminum metal matrix
Effect of chirality Index modulus slightly decreased as the diameter of the chiral carbon nanotubes increases.
Effect of chirality Index modulus slightly decreased as the diameter of the chiral carbon nanotubes increases.
Figure 5.15: Longitudinal Young's modulus for different chiral index carbon nanotube (at length Ic=5 nm) reinforced iron metal matrix
Figure 5.15: Longitudinal Young's modulus for different chiral index carbon nanotube (at length Ic=5 nm) reinforced iron metal matrix
5.9: Effect of chiral index on the Young’s modulus of copper matrix
5.9: Effect of chiral index on the Young’s modulus of copper matrix
Figure 5.16: Longitudinal Young's modulus for different chiral index carbon nanotube (at length Ic=8 nm) Reinforced iron metal matrix
Figure 5.16: Longitudinal Young's modulus for different chiral index carbon nanotube (at length Ic=8 nm) Reinforced iron metal matrix
Figure 5.17: Longitudinal Young's modulus for different chiral index carbon nanotube (at length Ic=3 nm) reinforced copper metal matrix
Figure 5.17: Longitudinal Young's modulus for different chiral index carbon nanotube (at length Ic=3 nm) reinforced copper metal matrix
Figure 5.18: Longitudinal Young's modulus for different chiral index carbon nanotube (at length Ic=5 nm) reinforced copper metal matrix
Figure 5.18: Longitudinal Young's modulus for different chiral index carbon nanotube (at length Ic=5 nm) reinforced copper metal matrix
Figure 5.20: Longitudinal Young's modulus for different chiral index carbon nanotube (at length Ic=3 nm) reinforced aluminum metal matrix
Figure 5.20: Longitudinal Young's modulus for different chiral index carbon nanotube (at length Ic=3 nm) reinforced aluminum metal matrix
Figure 5.22: Longitudinal Young's modulus for different chiral index carbon nanotube (at length Ilc=8 nm) reinforced aluminum metal matrix
Figure 5.22: Longitudinal Young's modulus for different chiral index carbon nanotube (at length Ilc=8 nm) reinforced aluminum metal matrix
‘igure 5.24: Transverse modulus for armchair carbon nanotube (5,5) (different length) reinforced iron metal matrix
‘igure 5.24: Transverse modulus for armchair carbon nanotube (5,5) (different length) reinforced iron metal matrix
Figure 5.25: Transverse modulus for chiral carbon nanotube (5, 10) (differen length) reinforced iron metal matrix
Figure 5.25: Transverse modulus for chiral carbon nanotube (5, 10) (differen length) reinforced iron metal matrix
carbon nanotube respectively when the volume fraction increases.
carbon nanotube respectively when the volume fraction increases.
igure 5.28: Transverse modulus for chiral carbon nanotube as short fiber reinforced copper metal matrix at different length
igure 5.28: Transverse modulus for chiral carbon nanotube as short fiber reinforced copper metal matrix at different length
sure 5.29; Transverse modulus for zigzag carbon nanotube at different length reinforced aluminum metal matrix
sure 5.29; Transverse modulus for zigzag carbon nanotube at different length reinforced aluminum metal matrix
‘igure 5.30: Transverse modulus for armchair carbon nanotube at different length reinforced aluminum metal matrix
‘igure 5.30: Transverse modulus for armchair carbon nanotube at different length reinforced aluminum metal matrix
‘igure 5.31: Transverse modulus for armchair carbon nanotube at different length reinforced aluminum metal matrix
‘igure 5.31: Transverse modulus for armchair carbon nanotube at different length reinforced aluminum metal matrix
nanotube type. The results show that the value of transverse modulus decreased as the
nanotube type. The results show that the value of transverse modulus decreased as the
respectively, when the volume fraction increases.
respectively, when the volume fraction increases.
Figure 5.33: Shear modulus for armchair carbon nanotube treated as short fiber reinforced iron matrix
Figure 5.33: Shear modulus for armchair carbon nanotube treated as short fiber reinforced iron matrix
Figure 5.34; Shear modulus for chiral carbon nanotube treated as short fiber reinforced iron matrix
Figure 5.34; Shear modulus for chiral carbon nanotube treated as short fiber reinforced iron matrix
Figure 5.35: Shear modulus for zigzag carbon nanotube treated as short fiber reinforced copper matrix at different length respectively, when the volume fraction increases.
Figure 5.35: Shear modulus for zigzag carbon nanotube treated as short fiber reinforced copper matrix at different length respectively, when the volume fraction increases.
Figure 5.38: Shear modulus for zigzag carbon nanotube treated as short fiber reinforced aluminum matrix at different length
Figure 5.38: Shear modulus for zigzag carbon nanotube treated as short fiber reinforced aluminum matrix at different length
‘igure 5.39: Shear modulus for armchair carbon nanotube (as short fiber) reinforced aluminum matrix at different length
‘igure 5.39: Shear modulus for armchair carbon nanotube (as short fiber) reinforced aluminum matrix at different length
‘igure 5.40: Shear modulus for chiral carbon nanotube treated as short fiber reinforced aluminum matrix at different length
‘igure 5.40: Shear modulus for chiral carbon nanotube treated as short fiber reinforced aluminum matrix at different length
chiral carbon nanotubes increases.
chiral carbon nanotubes increases.
The resulting volumes of overlapping
The resulting volumes of overlapping
The representative volume element is divided into many regular volumes for
The representative volume element is divided into many regular volumes for
corresponds to carbon nanotubes as shown in Figure 5.43.
corresponds to carbon nanotubes as shown in Figure 5.43.
shown in Figure 5.45.
shown in Figure 5.45.
6: Macro temperature imposed at boundary of the RVE representative volume element. Where AT denotes difference of uniform temperature at two opposite sides. L is the As result, effective conductivity is estimated by
6: Macro temperature imposed at boundary of the RVE representative volume element. Where AT denotes difference of uniform temperature at two opposite sides. L is the As result, effective conductivity is estimated by
Figure 5.47: Temperature and thermal flux distribution in the matrix and carbon nanotubes or Iron matrix respectively for the quarter model.
Figure 5.47: Temperature and thermal flux distribution in the matrix and carbon nanotubes or Iron matrix respectively for the quarter model.
‘igure 5.48: Temperature and thermal flux distribution in the matrix and carbon nanotubes or Copper matrix
‘igure 5.48: Temperature and thermal flux distribution in the matrix and carbon nanotubes or Copper matrix
‘igure 5.49: Temperature and thermal flux distribution in the matrix and carbon nanotubes or Aluminum matrix
‘igure 5.49: Temperature and thermal flux distribution in the matrix and carbon nanotubes or Aluminum matrix
quarter model. Figure 5.50: Temperature and thermal flux distribution in the matrix and carbon nanotubes or iron matrix (Model A)
quarter model. Figure 5.50: Temperature and thermal flux distribution in the matrix and carbon nanotubes or iron matrix (Model A)
Figure 5.51: Temperature and thermal flux distribution in the matrix and carbon nanotubes or Copper matrix
Figure 5.51: Temperature and thermal flux distribution in the matrix and carbon nanotubes or Copper matrix
Figure 5.52: Temperature and thermal flux distribution in the matrix and carbon nanotubes or Aluminum matrix
Figure 5.52: Temperature and thermal flux distribution in the matrix and carbon nanotubes or Aluminum matrix
figure 5.53: Temperature and thermal flux distribution in the matrix and carbon nanotubes or Iron matrix
figure 5.53: Temperature and thermal flux distribution in the matrix and carbon nanotubes or Iron matrix
Figure 5.54: Temperature and thermal flux distribution in the matrix and carbon nanotubes or Copper matrix
Figure 5.54: Temperature and thermal flux distribution in the matrix and carbon nanotubes or Copper matrix
b) Thermal flux
b) Thermal flux
As a result, the effective conductivity is estimated as follows. SSUM command is issued as shown in Figure 5.56 variables, then, new variable is defined by multiplying of these two variables and
As a result, the effective conductivity is estimated as follows. SSUM command is issued as shown in Figure 5.56 variables, then, new variable is defined by multiplying of these two variables and
Figures 5.57, 5.58, and 5.59 show the effect of volume fraction on the thermal
Figures 5.57, 5.58, and 5.59 show the effect of volume fraction on the thermal
5.18: Effect of chiral index of carbon nanotube reinforced copper matrix on the thermal conductivity for different models (Vi=3% )
5.18: Effect of chiral index of carbon nanotube reinforced copper matrix on the thermal conductivity for different models (Vi=3% )
57: Effect of thermal conductivity for zigzag carbon (as long fiber) nanotube reinforced iron metal matrix
57: Effect of thermal conductivity for zigzag carbon (as long fiber) nanotube reinforced iron metal matrix
sure 5.58: Effect of thermal conductivity for armchair carbon (as long fiber nanotube reinforced iron metal matrix
sure 5.58: Effect of thermal conductivity for armchair carbon (as long fiber nanotube reinforced iron metal matrix
Figure 5.61: Effect of thermal conductivity for armchair carbon (as long fiber) nanotube reinforced copper metal matrix
Figure 5.61: Effect of thermal conductivity for armchair carbon (as long fiber) nanotube reinforced copper metal matrix
Figures 5.63, 5.64, and 5.65 show the effect of volume fraction on the thermal
Figures 5.63, 5.64, and 5.65 show the effect of volume fraction on the thermal
Figure 5.62: Effect of thermal conductivity for chiral carbon (as long fiber) nanotube reinforced copper metal matrix
Figure 5.62: Effect of thermal conductivity for chiral carbon (as long fiber) nanotube reinforced copper metal matrix
Figure 5.63: Effect of thermal conductivity for zigzag carbon (as long fiber) nanotube reinforced aluminum metal matrix
Figure 5.63: Effect of thermal conductivity for zigzag carbon (as long fiber) nanotube reinforced aluminum metal matrix
Figure 5.65: Effect of thermal conductivity for chiral carbon (as long fiber) nanotube reinforced aluminum metal matrix
Figure 5.65: Effect of thermal conductivity for chiral carbon (as long fiber) nanotube reinforced aluminum metal matrix
have the biggest diameter.
have the biggest diameter.
Figure 5.67: Effect of volume fraction on the thermal conductivity of different carbon nanotube chiral index reinforced iron metal matrix ‘Model (B)’’
Figure 5.67: Effect of volume fraction on the thermal conductivity of different carbon nanotube chiral index reinforced iron metal matrix ‘Model (B)’’
Figure 5.68: Effect of volume fraction on the thermal conductivity of different carbon nanotube chiral index reinforced copper metal matrix ''Model (A)”
Figure 5.68: Effect of volume fraction on the thermal conductivity of different carbon nanotube chiral index reinforced copper metal matrix ''Model (A)”
ure 5.69: Effect of volume fraction on the thermal conductivity on different carbor nanotube chiral index reinforced copper metal matrix "Model (B)”
ure 5.69: Effect of volume fraction on the thermal conductivity on different carbor nanotube chiral index reinforced copper metal matrix "Model (B)”
pure 5.70: Effect of volume fraction on the thermal conductivity of different carbon nanotube chiral index reinforced aluminum metal matrix 'Model (A)”
pure 5.70: Effect of volume fraction on the thermal conductivity of different carbon nanotube chiral index reinforced aluminum metal matrix 'Model (A)”
ure 5.71: Effect of volume fraction on the thermal conductivity of different carbon nanotube chiral index reinforced aluminum metal matrix "Model (B)’’
ure 5.71: Effect of volume fraction on the thermal conductivity of different carbon nanotube chiral index reinforced aluminum metal matrix "Model (B)’’
For model “B”, Table 5.21 shows the results of thermal conductivity predicted for iron
For model “B”, Table 5.21 shows the results of thermal conductivity predicted for iron
pure 5.72: Effect of volume fraction on the thermal conductivity for armchair carbon nanotube reinforced iron metal matrix ‘Model (A)” nanocomposite varies linearly with the change in volume fractions within tested range.
pure 5.72: Effect of volume fraction on the thermal conductivity for armchair carbon nanotube reinforced iron metal matrix ‘Model (A)” nanocomposite varies linearly with the change in volume fractions within tested range.
Figure 5.73: Effect of volume fraction on the thermal conductivity for zigzag carbon nanotube reinforced iron metal matrix ‘Model (A)”
Figure 5.73: Effect of volume fraction on the thermal conductivity for zigzag carbon nanotube reinforced iron metal matrix ‘Model (A)”
Figure 5.74: Effect of volume fraction on the thermal conductivity for chiral carbon nanotube reinforced iron metal matrix ‘Model (A)”
Figure 5.74: Effect of volume fraction on the thermal conductivity for chiral carbon nanotube reinforced iron metal matrix ‘Model (A)”
‘igure 5.75: Effect of volume fraction on the thermal conductivity for chiral carbon nanotube reinforced iron metal matrix “Model (B)’’
‘igure 5.75: Effect of volume fraction on the thermal conductivity for chiral carbon nanotube reinforced iron metal matrix “Model (B)’’
‘igure 5.79: Effect of volume fraction on the thermal conductivity for zigzag carbon nanotube reinforced copper metal matrix “Model (A)”’
‘igure 5.79: Effect of volume fraction on the thermal conductivity for zigzag carbon nanotube reinforced copper metal matrix “Model (A)”’
Figure 5.80: Effect of volume fraction on the thermal conductivity for chiral carbon nanotube reinforced copper metal matrix “Model (A)”’
Figure 5.80: Effect of volume fraction on the thermal conductivity for chiral carbon nanotube reinforced copper metal matrix “Model (A)”’
Figure 5.81: Effect of volume fraction on the thermal conductivity for armchair carbon nanotube reinforced copper metal matrix “Model (B)”
Figure 5.81: Effect of volume fraction on the thermal conductivity for armchair carbon nanotube reinforced copper metal matrix “Model (B)”
igure 5.82: Effect of volume fraction on the thermal conductivity for zigzag carbo1 nanotube reinforced copper metal matrix “Model (B)”
igure 5.82: Effect of volume fraction on the thermal conductivity for zigzag carbo1 nanotube reinforced copper metal matrix “Model (B)”
Figure 5.83: Effect of volume fraction on the thermal conductivity for chiral carbon nanotube reinforced copper metal matrix “Model (B)”
Figure 5.83: Effect of volume fraction on the thermal conductivity for chiral carbon nanotube reinforced copper metal matrix “Model (B)”
For Model “B”, Table 5.25 shows the results of thermal conductivity predicted for
For Model “B”, Table 5.25 shows the results of thermal conductivity predicted for
5: Effect of chiral index diameter of carbon nanotube on the thermal conductivity for reinforcing aluminum matrix “Model (B)”’ (V;=3%)
5: Effect of chiral index diameter of carbon nanotube on the thermal conductivity for reinforcing aluminum matrix “Model (B)”’ (V;=3%)
‘igure 5.84: Effect of volume fraction on the thermal conductivity for armchair carbon nanotube reinforced aluminum metal matrix “Model (A)” the Nanocomposite varies linearly with the change in volume fractions.
‘igure 5.84: Effect of volume fraction on the thermal conductivity for armchair carbon nanotube reinforced aluminum metal matrix “Model (A)” the Nanocomposite varies linearly with the change in volume fractions.
igure 5.85: Effect of volume fraction on the thermal conductivity for zigzag carbon nanotube reinforced aluminum metal matrix “Model (A)”’
igure 5.85: Effect of volume fraction on the thermal conductivity for zigzag carbon nanotube reinforced aluminum metal matrix “Model (A)”’
Effect of volume fraction on the thermal conductivity for chiral carbor nanotube reinforced aluminum metal matrix ‘““Model (A)’’ Effect of volume fraction on the thermal conductivity for chiral carbon nanotube reinforced aluminum metal matrix “Model (B)””
Effect of volume fraction on the thermal conductivity for chiral carbor nanotube reinforced aluminum metal matrix ‘““Model (A)’’ Effect of volume fraction on the thermal conductivity for chiral carbon nanotube reinforced aluminum metal matrix “Model (B)””
Effect of volume fraction on the thermal conductivity for armchair carbon nanotube reinforced aluminum metal matrix “Model (B)’’
Effect of volume fraction on the thermal conductivity for armchair carbon nanotube reinforced aluminum metal matrix “Model (B)’’
Effect of volume fraction on the thermal conductivity for zigzag carbon nanotube reinforced aluminum metal matrix ‘Model (B)””
Effect of volume fraction on the thermal conductivity for zigzag carbon nanotube reinforced aluminum metal matrix ‘Model (B)””
Effect of carbon nanotube diameter on the thermal conductivity for reinforcing iron metal matrix "Model (B)”
Effect of carbon nanotube diameter on the thermal conductivity for reinforcing iron metal matrix "Model (B)”
92: Effect of carbon nanotube diameter on the thermal conductivity for reinforcing copper metal matrix ''Model (A)”
92: Effect of carbon nanotube diameter on the thermal conductivity for reinforcing copper metal matrix ''Model (A)”
Effect of carbon nanotube diameter on the thermal conductivity for reinforcing copper metal matrix ''Model (B)’”’
Effect of carbon nanotube diameter on the thermal conductivity for reinforcing copper metal matrix ''Model (B)’”’
D4: Effect of carbon nanotube diameter on the thermal conductivity for reinforcing aluminum metal matrix ''Model (A)”
D4: Effect of carbon nanotube diameter on the thermal conductivity for reinforcing aluminum metal matrix ''Model (A)”
5: Effect of carbon nanotube diameter on the thermal conductivity for reinforcing aluminum metal matrix 'Model (B)”
5: Effect of carbon nanotube diameter on the thermal conductivity for reinforcing aluminum metal matrix 'Model (B)”
Effect of thermal contact conductance on thermal conductivity for armchair carbon nanotube reinforced iron matrix at different length: (a) Model (A), and (b) Model (B)
Effect of thermal contact conductance on thermal conductivity for armchair carbon nanotube reinforced iron matrix at different length: (a) Model (A), and (b) Model (B)
thermal conductivity for model “A” and Model “B”, respectively. It can be observed
thermal conductivity for model “A” and Model “B”, respectively. It can be observed
igure 5.96: Effect of thermal contact conductance on thermal conductivity for armchair carbon nanotube (5, 5) reinforced iron metal matrix (Model “A’’)
igure 5.96: Effect of thermal contact conductance on thermal conductivity for armchair carbon nanotube (5, 5) reinforced iron metal matrix (Model “A’’)
Effect of thermal contact conductance on thermal conductivity for armchair carbon nanotube (5, 5) reinforced iron metal matrix (Model ‘‘B’’)
Effect of thermal contact conductance on thermal conductivity for armchair carbon nanotube (5, 5) reinforced iron metal matrix (Model ‘‘B’’)
Effect of thermal contact conductance on thermal conductivity for zigzag carbon nanotube reinforced iron matrix at different length: (a) Model (A), and (b) Model (B)
Effect of thermal contact conductance on thermal conductivity for zigzag carbon nanotube reinforced iron matrix at different length: (a) Model (A), and (b) Model (B)
re 5.99: Effect of thermal contact conductance on thermal conductivity for zigzag carbon nanotube (5, 0) reinforced iron metal matrix (Model “B”’)
re 5.99: Effect of thermal contact conductance on thermal conductivity for zigzag carbon nanotube (5, 0) reinforced iron metal matrix (Model “B”’)
Figures 5.100 and 5.101 show the effect of thermal contact conductance on the thermal
Figures 5.100 and 5.101 show the effect of thermal contact conductance on the thermal
re5.102: Effect of thermal contact on thermal conductivity for different chiral Index carbon nanotube reinforced iron metal matrix (1, =3 nm)
re5.102: Effect of thermal contact on thermal conductivity for different chiral Index carbon nanotube reinforced iron metal matrix (1, =3 nm)
> 5.103: Effect of thermal contact on thermal conductivity for different chiral index carbon nanotube reinforced iron metal matrix (1. =5 nm)
> 5.103: Effect of thermal contact on thermal conductivity for different chiral index carbon nanotube reinforced iron metal matrix (1. =5 nm)
length of carbon nanotubes increased the thermal conductivity also increased.
length of carbon nanotubes increased the thermal conductivity also increased.
Effect of thermal contact conductance on thermal conductivity for armchair carbon nanotube (5, 5) reinforced copper metal matrix (MODEL “B’’)
Effect of thermal contact conductance on thermal conductivity for armchair carbon nanotube (5, 5) reinforced copper metal matrix (MODEL “B’’)
Figures 5.107 and 5.108 show the effect of thermal contact conductance on the thermal
Figures 5.107 and 5.108 show the effect of thermal contact conductance on the thermal
Effect of thermal contact conductance on thermal conductivity for zigzag carbon nanotube (5, 0) reinforced copper metal matrix (Model “B’’)
Effect of thermal contact conductance on thermal conductivity for zigzag carbon nanotube (5, 0) reinforced copper metal matrix (Model “B’’)
Effect of thermal contact conductance on thermal conductivity for chiral carbon nanotube (5, 10) reinforced copper metal matrix (Model “‘B’’)
Effect of thermal contact conductance on thermal conductivity for chiral carbon nanotube (5, 10) reinforced copper metal matrix (Model “‘B’’)
112: Effect of thermal contact on thermal conductivity for different chiral index carbon nanotube reinforced copper metal matrix (1. =5 nm) Effect of thermal contact on thermal conductivity for different chiral index carbon nanotube reinforced copper metal matrix (1. =8 nm)
112: Effect of thermal contact on thermal conductivity for different chiral index carbon nanotube reinforced copper metal matrix (1. =5 nm) Effect of thermal contact on thermal conductivity for different chiral index carbon nanotube reinforced copper metal matrix (1. =8 nm)
conductivity for Model “A” and Model “B”, respectively. It can be observed that as the Effect of thermal contact conductance on thermal conductivity for armchair carbon nanotube (5, 5) reinforced aluminum metal matrix (Model “‘B’’)
conductivity for Model “A” and Model “B”, respectively. It can be observed that as the Effect of thermal contact conductance on thermal conductivity for armchair carbon nanotube (5, 5) reinforced aluminum metal matrix (Model “‘B’’)
length of carbon nanotubes increased the thermal conductivity also increased.
length of carbon nanotubes increased the thermal conductivity also increased.
Figures 5.116 and 5.117 show the effect of thermal contact conductance on the thermal
Figures 5.116 and 5.117 show the effect of thermal contact conductance on the thermal
gure 5.116: Effect of thermal contact conductance on thermal conductivity for zigzag carbon nanotube (5, 0) reinforced aluminum metal matrix (Model “A”’)
gure 5.116: Effect of thermal contact conductance on thermal conductivity for zigzag carbon nanotube (5, 0) reinforced aluminum metal matrix (Model “A”’)
Effect of thermal contact conductance on thermal conductivity for zigzag carbon nanotube (5, 0) reinforced aluminum metal matrix (Model “B’’)
Effect of thermal contact conductance on thermal conductivity for zigzag carbon nanotube (5, 0) reinforced aluminum metal matrix (Model “B’’)
); Effect of thermal contact conductance on thermal conductivity for chiral carbon nanotube (5, 10) reinforced aluminum metal matrix (Model “B’’) 18: Effect of thermal contact conductance on thermal conductivity for chiral carbon nanotube (5, 10) reinforced aluminum metal matrix (Model “A’’)
); Effect of thermal contact conductance on thermal conductivity for chiral carbon nanotube (5, 10) reinforced aluminum metal matrix (Model “B’’) 18: Effect of thermal contact conductance on thermal conductivity for chiral carbon nanotube (5, 10) reinforced aluminum metal matrix (Model “A’’)
Effect of thermal contact on thermal conductivity for different chiral Index carbon nanotube reinforced aluminum metal matrix (1, =3 nm)
Effect of thermal contact on thermal conductivity for different chiral Index carbon nanotube reinforced aluminum metal matrix (1, =3 nm)
Effect of thermal contact on thermal conductivity for different chiral Index carbon nanotube reinforced aluminum metal matrix (1, =5 nm)
Effect of thermal contact on thermal conductivity for different chiral Index carbon nanotube reinforced aluminum metal matrix (1, =5 nm)
[22: Effect of thermal contact on thermal conductivity for different chiral Index carbon nanotube reinforced aluminum metal matrix (1. =8 nm)
[22: Effect of thermal contact on thermal conductivity for different chiral Index carbon nanotube reinforced aluminum metal matrix (1. =8 nm)
Validation of elastic properties for carbon nanotube reinforced iron metal matrix Figure 6.1: Longitudinal Young's modulus for carbon nanotube reinforced Iron metal matrix validation
Validation of elastic properties for carbon nanotube reinforced iron metal matrix Figure 6.1: Longitudinal Young's modulus for carbon nanotube reinforced Iron metal matrix validation
ure 6.2: Transverse Young's modulus for carbon nanotube reinforced iron metal matrix validation
ure 6.2: Transverse Young's modulus for carbon nanotube reinforced iron metal matrix validation
pure 6.4: Major Poisson’s ratio for carbon nanotube reinforced iron metal matrix validation
pure 6.4: Major Poisson’s ratio for carbon nanotube reinforced iron metal matrix validation
Figure 6.5: Longitudinal Young's modulus for carbon nanotube reinforced copper metal matrix validation Validation of elastic properties for carbon nanotube reinforced copper metal matrix
Figure 6.5: Longitudinal Young's modulus for carbon nanotube reinforced copper metal matrix validation Validation of elastic properties for carbon nanotube reinforced copper metal matrix
sure 6.6: Transverse modulus for carbon nanotube reinforced copper metal matrix validation
sure 6.6: Transverse modulus for carbon nanotube reinforced copper metal matrix validation
Figure 6.7: Shear modulus for carbon nanotube reinforced copper metal matri validation
Figure 6.7: Shear modulus for carbon nanotube reinforced copper metal matri validation
Validation of elastic properties for carbon nanotube reinforced aluminum metal matrix
Validation of elastic properties for carbon nanotube reinforced aluminum metal matrix
Figure 6.11: Shear modulus for carbon nanotube reinforced aluminum metal matrix validation
Figure 6.11: Shear modulus for carbon nanotube reinforced aluminum metal matrix validation
Figure 6.15: Validation of longitudinal Young's modulus for chiral (5, 10) carbon nanotubes reinforced iron metal matrix (lc=3nm)
Figure 6.15: Validation of longitudinal Young's modulus for chiral (5, 10) carbon nanotubes reinforced iron metal matrix (lc=3nm)
Figure 6.16: Validation of longitudinal Young's modulus for armchair (5, 5) carbon nanotubes reinforced copper metal matrix (Ic=3nm)
Figure 6.16: Validation of longitudinal Young's modulus for armchair (5, 5) carbon nanotubes reinforced copper metal matrix (Ic=3nm)
igure 6.18: Validation of longitudinal Young's modulus for chiral (5, 10) carbo nanotubes reinforced copper metal matrix (lc=3nm)
igure 6.18: Validation of longitudinal Young's modulus for chiral (5, 10) carbo nanotubes reinforced copper metal matrix (lc=3nm)
‘igure 6.21: Validation of longitudinal Young's modulus for chiral (5, 10) carbor nanotubes reinforced aluminum metal matrix (lce=3nm)
‘igure 6.21: Validation of longitudinal Young's modulus for chiral (5, 10) carbor nanotubes reinforced aluminum metal matrix (lce=3nm)
Validation of transverse modulus for carbon nanotubes treated as short fiber reinforced iron metal matrix
Validation of transverse modulus for carbon nanotubes treated as short fiber reinforced iron metal matrix
Figure 6.23: Validation of transverse modulus for carbon nanotubes treated as short fiber reinforced copper metal matrix
Figure 6.23: Validation of transverse modulus for carbon nanotubes treated as short fiber reinforced copper metal matrix
Figure 6.24: Validation of transverse modulus for carbon nanotubes treated as short fiber reinforced aluminum metal matrix
Figure 6.24: Validation of transverse modulus for carbon nanotubes treated as short fiber reinforced aluminum metal matrix
Figure 6.25: Validation of shear modulus for carbon nanotubes treated as short fiber reinforced iron metal matrix
Figure 6.25: Validation of shear modulus for carbon nanotubes treated as short fiber reinforced iron metal matrix
Figure 6.27: Validation of shear modulus for carbon nanotubes treated as short fiber reinforced aluminum metal matrix
Figure 6.27: Validation of shear modulus for carbon nanotubes treated as short fiber reinforced aluminum metal matrix
Figure 6.28: Comparison between the thermal conductivity models for carbon nanotube reinforced aluminum matrix predictions may be close to actual values of the effective longitudinal conductivity.
Figure 6.28: Comparison between the thermal conductivity models for carbon nanotube reinforced aluminum matrix predictions may be close to actual values of the effective longitudinal conductivity.
Figure 6.29: Comparison between the thermal conductivity models for carbon nanotube reinforced copper matrix
Figure 6.29: Comparison between the thermal conductivity models for carbon nanotube reinforced copper matrix
Figure 6.31: Validation of thermal conductivity of armchair carbon nanotube treated as long fiber reinforced iron metal matrix
Figure 6.31: Validation of thermal conductivity of armchair carbon nanotube treated as long fiber reinforced iron metal matrix
Figure 6.33: Validation of thermal conductivity of chiral carbon nanotube treated as long fiber reinforced iron metal matrix
Figure 6.33: Validation of thermal conductivity of chiral carbon nanotube treated as long fiber reinforced iron metal matrix
Figure 6.34: Validation of thermal conductivity of armchair carbon nanotube treated as long fiber reinforced copper metal matrix
Figure 6.34: Validation of thermal conductivity of armchair carbon nanotube treated as long fiber reinforced copper metal matrix
figure 6.35: Validation of thermal conductivity of zigzag carbon nanotube treated as long fiber reinforced copper metal matrix
figure 6.35: Validation of thermal conductivity of zigzag carbon nanotube treated as long fiber reinforced copper metal matrix
Figure 6.36: Validation of thermal conductivity of chiral carbon nanotube treated as long fiber reinforced copper metal matrix
Figure 6.36: Validation of thermal conductivity of chiral carbon nanotube treated as long fiber reinforced copper metal matrix
The deviation percentage were calculated for all cases and presented in Tables 6.11 (a), Finite element predictions for the two models show higher value than theoretical results.
The deviation percentage were calculated for all cases and presented in Tables 6.11 (a), Finite element predictions for the two models show higher value than theoretical results.
Figure 6.37: Validation of thermal conductivity of armchair carbon nanotube treated as long fiber reinforced aluminum metal matrix
Figure 6.37: Validation of thermal conductivity of armchair carbon nanotube treated as long fiber reinforced aluminum metal matrix
‘igure 6.38: Validation of thermal conductivity of zigzag carbon nanotube treated as long fiber reinforced aluminum metal matrix
‘igure 6.38: Validation of thermal conductivity of zigzag carbon nanotube treated as long fiber reinforced aluminum metal matrix
Figure 6.39: Validation of thermal conductivity of chiral carbon nanotube treated as long fiber reinforced aluminum metal matrix
Figure 6.39: Validation of thermal conductivity of chiral carbon nanotube treated as long fiber reinforced aluminum metal matrix
Figure 6.40: Validation of thermal conductivity for armchair (5, 5) carbon nanotubes (as short fiber "1.=3'') reinforced iron metal matrix
Figure 6.40: Validation of thermal conductivity for armchair (5, 5) carbon nanotubes (as short fiber "1.=3'') reinforced iron metal matrix
Figure 6.46: Validation of thermal conductivity for armchair (5, 5) carbon nanotubes (as short fiber ''l-=3"') reinforced aluminum metal matrix
Figure 6.46: Validation of thermal conductivity for armchair (5, 5) carbon nanotubes (as short fiber ''l-=3"') reinforced aluminum metal matrix
‘igure 6.49: Validation of thermal conductivity for armchair (5, 5) carbon nanotubes (as short fiber) reinforced iron metal matrix at different lengths
‘igure 6.49: Validation of thermal conductivity for armchair (5, 5) carbon nanotubes (as short fiber) reinforced iron metal matrix at different lengths
in Tables 6.16 (a), (b), and (c), respectively.
in Tables 6.16 (a), (b), and (c), respectively.
‘igure 6.52: Validation of thermal conductivity for armchair (5, 5) carbon nanotubes (as short fiber) reinforced copper metal matrix at different lengths ‘igure 6.53: Validation of thermal conductivity for zigzag (5, 0) carbon nanotubes (as short fiber) reinforced copper metal matrix at different lengths
‘igure 6.52: Validation of thermal conductivity for armchair (5, 5) carbon nanotubes (as short fiber) reinforced copper metal matrix at different lengths ‘igure 6.53: Validation of thermal conductivity for zigzag (5, 0) carbon nanotubes (as short fiber) reinforced copper metal matrix at different lengths
‘igure 6.56: Validation of thermal conductivity for zigzag (5, 0) carbon nanotubes (as short fiber) reinforced aluminum metal matrix at different lengths
‘igure 6.56: Validation of thermal conductivity for zigzag (5, 0) carbon nanotubes (as short fiber) reinforced aluminum metal matrix at different lengths
Figure 6.57: Validation of thermal conductivity for chiral (5, 10) carbon nanotubes (as short fiber) reinforced aluminum metal matrix at different lengths
Figure 6.57: Validation of thermal conductivity for chiral (5, 10) carbon nanotubes (as short fiber) reinforced aluminum metal matrix at different lengths
Figure 6.59: Validation of thermal conductivity for carbon nanotubes (as Short Fiber) reinforced iron metal matrix at different diameters and at l= 5nm
Figure 6.59: Validation of thermal conductivity for carbon nanotubes (as Short Fiber) reinforced iron metal matrix at different diameters and at l= 5nm
Figure 6.61: Validation of thermal conductivity carbon nanotubes (as Short Fiber) reinforced Copper metal matrix at different diameters and at 1= 3nm
Figure 6.61: Validation of thermal conductivity carbon nanotubes (as Short Fiber) reinforced Copper metal matrix at different diameters and at 1= 3nm
igure 6.62: Validation of thermal conductivity for carbon nanotubes (as Short Fiber) reinforced Copper metal matrix at different diameters and at ]= 5nm
igure 6.62: Validation of thermal conductivity for carbon nanotubes (as Short Fiber) reinforced Copper metal matrix at different diameters and at ]= 5nm
Figure 6.64: Validation of thermal conductivity carbon nanotubes (as Short Fiber reinforced Aluminum metal matrix at different diameters and at l= 3nm
Figure 6.64: Validation of thermal conductivity carbon nanotubes (as Short Fiber reinforced Aluminum metal matrix at different diameters and at l= 3nm
Figure 6.65: Validation of thermal conductivity carbon nanotubes (as Short Fiber) reinforced Aluminum metal matrix at different diameters and at l= 5nm
Figure 6.65: Validation of thermal conductivity carbon nanotubes (as Short Fiber) reinforced Aluminum metal matrix at different diameters and at l= 5nm
‘igure 6.67: Validation of thermal contact conductance for armchair (5, 5) carbon nanotubes (as Short Fiber) reinforced Iron metal matrix
‘igure 6.67: Validation of thermal contact conductance for armchair (5, 5) carbon nanotubes (as Short Fiber) reinforced Iron metal matrix
Figure 6.69: Validation of thermal contact conductance for chiral (5, 10) carbon nanotubes (as Short Fiber) reinforced iron metal
Figure 6.69: Validation of thermal contact conductance for chiral (5, 10) carbon nanotubes (as Short Fiber) reinforced iron metal
Figure 6.71: Validation of thermal contact conductance for zigzag (5, 0) for carbon nanotubes (as short fiber) reinforced copper metal matrix
Figure 6.71: Validation of thermal contact conductance for zigzag (5, 0) for carbon nanotubes (as short fiber) reinforced copper metal matrix
Figure 6.72: Validation of thermal contact conductance for chiral (5, 10) carbon nanotubes (as Short Fiber) reinforced copper metal matrix
Figure 6.72: Validation of thermal contact conductance for chiral (5, 10) carbon nanotubes (as Short Fiber) reinforced copper metal matrix
Figure 6.73: Validation of thermal contact conductance for armchair (5, 5) carbon nanotubes (as short fiber) reinforced aluminum metal matrix
Figure 6.73: Validation of thermal contact conductance for armchair (5, 5) carbon nanotubes (as short fiber) reinforced aluminum metal matrix
Figure 6.75: Validation of thermal contact conductance for chiral (5, 10) carbon nanotubes (as Short Fiber) reinforced aluminum metal matrix
Figure 6.75: Validation of thermal contact conductance for chiral (5, 10) carbon nanotubes (as Short Fiber) reinforced aluminum metal matrix

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  106. Kane, D., Micolich, A., and Roger, P.: 'Nanomaterials Science and Applications' (Taylor & Francis Group, LLC, 2016)
  107. Musa, S.M.: 'Computational Finite Element Methods in Nanotechnology' (CRC Press, 2013)
  108. Kaveh, A.: 'Computational Structural Analysis and Finite Element Methods' (Springler, 2014)
  109. Fan, C.-W., Huang, J.-H., Hwu, C., and Liu, Y.-Y.: 'Mechanical Properties of Single-walled Carbon Nanotubes -A Finite Element Approach', Advanced Materials Research, 2008, 33-37, pp. 937-942
  110. Kalamkarov, A.L., Georgiades, A.V., Rokkam, S.K., Veedu, V.P., and Ghasemi- Nejhad, M.N.: 'Analytical and Numerical Techniques to Predict Carbon Nanotubes Properties', International Journal of Solids and Structures, 2006, 43, pp. 6832-6854
  111. Ávila, A.F., and Lacerda, G.S.R.: 'Molecular Mechanics Applied to Single- Walled Carbon Nanotubes', Materials Research, 2008, 11, (3), pp. 325-333
  112. Hu, N.: 'Composites and Their Properties' ( InTech, 2012)
  113. Islam, M.S., and Szpunar, J.: 'Effects of Orientation of Carbon Nanotubes on CNT Bundle Based Silk Composite Using Finite Element Method', Modeling and Numerical Simulation of Material Science, 2013, (3), pp. 33-38
  114. Rémond, Y., Ahzi, S., Baniassadi, M., and Garmestani, H.: 'Applied RVE Reconstruction and Homogenization of Heterogeneous Materials ' (John Wiley & Sons, Inc. and ISTE Ltd 2016)
  115. Liu, Y.J., and Chen, X.L.: 'Continuum Models of Carbon Nanotube-Based Composites Using the Boundary Element Method', Electronic Journal of Boundary Elements, 2003, 1, (2), pp. 316-335
  116. Islam, M.S., Riktan, F.O., Chowdhury, S.C., Chowdhury, M.M.R., and Ahmed, S.: 'Evaluation of Tensile Modulus of Carbon Nanotube Bundle Based Composite with Interface Using Finite Element Method'. Proc. 2011 COMSOL Conference, Banglore2011
  117. Husain, M., and Khan, Z.H.: 'Advanced Nanomaterials' (Springer 2016)
  118. Freitag, M., Tsang, J.C., Kirtley, J., Carlsen, A., Chen, J., Troeman, A., Hilgenkamp, H., and Avouris, P.: 'Electrically Excited, Localized Infrared Emission From Single Carbon Nanotubes', Nano Letters, 2006, 6, (7), pp. 1425- 1433
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  123. Lee, H.-H.: 'Finite Element Simulations with ANSYS Workbench 14' (SDC Publications, 2012)
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  128. Alawadhi, E.M.: 'Finite Element Simulations Using ANSYS' (CRC Press 2010)
  129. Chen, X., and Liu, Y.: 'Finite Element Modeling and Simulation with ANSYS Workbench' (CRC Press 2015)
  130. Rangel, J.H., Brostow, W., and Castlano, V.M.: 'Mechanical modeling of single- walled carbon nanotube using finite element approach', Polimery, 2013, 58, (4), pp. 276-281
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  136. Carbon Nanotubes and Their Composites: A Review. Sudan Engineering Society Journal, vol. 58, no. 1, March 2012.
  137. Carbon Nanotubes: Challenges and Opportunities. Proceedings of International Conference on Computing, Electrical and Electronic Engineering (ICCEEE 2013), 26-28 August 2013, Khartoum, Sudan
  138. Determination of Elastic Properties of Carbon Nanotubes Treated as Long Fiber for Reinforcing Iron Matrix", 1st Conference of Industrial Technology (CIT2017) 17-18 May 2017, Misrata, Libya
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