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In this paper, the mechanical, thermal and electrical properties of carbon fiber modified thermoplastic polyimide were numerically analyzed by finite element analysis. A three-dimensional model was created, in which continuous carbon fibers are aligning and paralleling to each other and uniformly distributing in the polymer matrix. The behaviors of the composites in two extreme situations, i.e., parallel or perpendicular to carbon fiber direction, were simulated. The effects of the volume fraction of carbon fiber content on the physical properties were investigated. It shows clearly that carbon fibers significantly improve the mechanical strength, and thermal and electrical conductivities. The future work includes investigation of the physical properties of the conductive network of the composites with random carbon fiber orientation, and different fillers, such as graphite, and carbon nanotubes.
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*Corresponding author (Z. Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878. E-mail address: [email protected] . 2013. American Transactions on Engineering & Applied Sciences. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/133-148.pdf 133 American Transactions on Engineering & Applied Sciences http://TuEngr.com/ATEAS Characterization of Mechanical, Thermal, and Electrical Properties of Carbon Fiber Polymer Composites by Modeling Zhong Hu a* , Xingzhong Yan b , James Wu c , and Michelle Manzo c a Department of Mechanical Engineering, South Dakota State University, USA b Department of Electrical Engineering &Computer Science, South Dakota State University, USA c Electrochemistry Branch, NASA Glenn Research Center, USA A R T I C L E I N F O A B S T RA C T Article history: Received February 06, 2013 Received in revised form March 06, 2013 Accepted March 08, 2013 Available online March 11, 2013 Keywords: Carbon Fibers Polymer Composites Physical Properties Characterization Finite Element Analysis In this paper, the mechanical, thermal and electrical properties of carbon fiber modified thermoplastic polyimide were numerically analyzed by finite element analysis. A three-dimensional model was created, in which continuous carbon fibers are aligning and paralleling to each other and uniformly distributing in the polymer matrix. The behaviors of the composites in two extreme situations, i.e., parallel or perpendicular to carbon fiber direction, were simulated. The effects of the volume fraction of carbon fiber content on the physical properties were investigated. It shows clearly that carbon fibers significantly improve the mechanical strength, and thermal and electrical conductivities. The future work includes investigation of the physical properties of the conductive network of the composites with random carbon fiber orientation, and different fillers, such as graphite, and carbon nanotubes. 2013 American Transactions on Engineering & Applied Sciences. 2013 American Transactions on Engineering & Applied Sciences.
Transcript
Page 1: Characterization of Mechanical, Thermal, and Electrical Properties of Carbon Fiber Polymer Composites by Modeling

*Corresponding author (Z. Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878. E-mail address: [email protected]. 2013. American Transactions on Engineering & Applied Sciences. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/133-148.pdf

133

American Transactions on Engineering & Applied Sciences

http://TuEngr.com/ATEAS

Characterization of Mechanical, Thermal, and Electrical Properties of Carbon Fiber Polymer Composites by Modeling

Zhong Hu a*, Xingzhong Yan b, James Wu c, and Michelle Manzo c

a Department of Mechanical Engineering, South Dakota State University, USA b Department of Electrical Engineering &Computer Science, South Dakota State University, USA c Electrochemistry Branch, NASA Glenn Research Center, USA A R T I C L E I N F O

A B S T RA C T

Article history: Received February 06, 2013 Received in revised form March 06, 2013 Accepted March 08, 2013 Available online March 11, 2013 Keywords: Carbon Fibers Polymer Composites Physical Properties Characterization Finite Element Analysis

In this paper, the mechanical, thermal and electrical properties of carbon fiber modified thermoplastic polyimide were numerically analyzed by finite element analysis. A three-dimensional model was created, in which continuous carbon fibers are aligning and paralleling to each other and uniformly distributing in the polymer matrix. The behaviors of the composites in two extreme situations, i.e., parallel or perpendicular to carbon fiber direction, were simulated. The effects of the volume fraction of carbon fiber content on the physical properties were investigated. It shows clearly that carbon fibers significantly improve the mechanical strength, and thermal and electrical conductivities. The future work includes investigation of the physical properties of the conductive network of the composites with random carbon fiber orientation, and different fillers, such as graphite, and carbon nanotubes.

2013 American Transactions on Engineering & Applied Sciences.

2013 American Transactions on Engineering & Applied Sciences.

Page 2: Characterization of Mechanical, Thermal, and Electrical Properties of Carbon Fiber Polymer Composites by Modeling

134 Zhong Hu, Xinghong Yan, James Wu, and Michelle Manzo

1. Introduction

Polymers are lightweight, flexible, resistant to heat and chemicals, and non-conductive and

transparent to electromagnetic radiation. Therefore, they are used in the electronics industry for

flexible cables, as an insulating film, and for medical tubing. Thus, they are not suitable for use as

enclosures for electronic equipment because they cannot shield it from outside radiation. Also they

cannot prevent the escape of radiation from the component. (Elimat et al. 2010; Navin and Deepak

2004) Several fillers can be added to the insulating polymeric matrix in order to achieve different

conductivity ranges for a variety of industrial applications. (Delmonte 1990; Neelakanta 1995)

Polyacrylonitrile (PAN)-based carbon fibers (CFs) possess high stiffness and strength, low

expansion coefficient, and elevated thermal and electric conductivity measured along the fiber

direction. (Lei et al. 2008; Donnet et al. 1990; Park and Chou 2000; Chand 2000) Carbon fiber

(CF)/polymer composites are used in the aerospace industry on account of their high-specific

stiffness and strength, which are higher than in metallic materials. (Surendra et al. 2009)

Conducting polymers have been extensively studied because of their potential applications in

light-emitting devices, batteries, electromagnetic shield, and other functional applications.

(Anupama et al. 2010; Tsotra and Friedrich 2003; Tse et al. 1981) The ability of these composites

to serve as capacitors and other circuit element means that the structures is itself the electronics, so

that the electronics 'vanish' into the structure. (Luo and Chung 2001) In the case of continuous CF

polymer-matrix composites, CFs are the conductors (resistors) and they can be intercalated to

become electron metals or hole metals. (Chung and Wang 1999) By having the electronics vanish

into the structure, space is saved. The space saving is particularly valuable for capacitors of large

capacitance in space applications. In addition to space saving, structural electronics have the

advantage of being mechanically rugged and inexpensive, since structural materials are

necessarily rugged and inexpensive. The use of a structure as a capacitor is particularly valuable in

conjunction with structures that are powered by solar cells, as the structure (capacitor) can be used

to store the electrical energy generated by the solar cells. (Luo and Chung 2001; Chung and Wang

1999; Zhu et al. 2011; Stoller and Ruoff 2010).

In this paper, the mechanical, thermal and electrical properties of CF modified polyimide (PI)

matrix composite will be numerically analyzed by finite element analysis (FEA). (Herakovich

1998; Minus and Kumar 2007; Fei et al. 2007) A three-dimensional model will be created, in

Page 3: Characterization of Mechanical, Thermal, and Electrical Properties of Carbon Fiber Polymer Composites by Modeling

*Corresponding author (Z. Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878. E-mail address: [email protected]. 2013. American Transactions on Engineering & Applied Sciences. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/133-148.pdf

135

which continuous CFs will be aligning and paralleling to each other and uniformly distributing in

the matrix. The behaviors of the composite in two extreme situations, i.e., parallel or

perpendicular to the CF direction, will be simulated. The effects of CF volumetric fraction on the

physical (mechanical, thermal, and electrical) properties will be investigated.

2. Modeling by Finite Element Analysis

Although the material properties for the composite are anisotropic, for each component (CF

filler or polymer matrix) they could be treated as isotropic. Assuming that each set of properties

(mechanical, thermal, or electrical properties) is independent. Therefore, each set of the

properties can be evaluated separately. For mechanical properties, a linear and elastic stress-strain

relationship is assumed. Therefore, for each element of one kind material (CF filler or polymer

matrix), the structural governing equation is (ANSYS Inc. 2012) (1) where is the stress vector, is the elastic strain vector, and is the elastic stiffness

matrix. For thermal properties, the heat transfer governing equation of conduction at steady-state is 0 (2) where is the heat flux vector, is the vector operator, T is temperature, and is the

thermal conductivity matrix. For electrical properties, the electromagnetic field governing

equations are matrix. For electrical properties, the electromagnetic field governing equations are

; ; · 0; · (3) where is curl operator, · is divergence operator, is the magnetic field intensity vector,

is the total current density vector, is the electric flux density vector, t is time, is the

electric field intensity vector, is the magnetic flux density vector, and ρe is the electric charge

density.

Therefore, each element formulations can be developed and the equations for each element can

Page 4: Characterization of Mechanical, Thermal, and Electrical Properties of Carbon Fiber Polymer Composites by Modeling

136 Zhong Hu, Xinghong Yan, James Wu, and Michelle Manzo

be assembled into global matrix for the entire domain of the composite (including both CF filler

and polymer matrix). In this work, a commercial FEA software ANSYS was used. A

three-dimensional element SOLID223, i.e., a 3-D 20-node high-order accuracy coupled–field

(structural, thermal, and electrical) solid element was adopted. The isotropic properties of each

material component were assumed. PAN-based carbon fibers with filament size of 5μm in

diameter are chosen as polymeric matrix filler and polyimides as polymeric matrix. The physical

properties of both materials are listed in Table 1. (Herakovich 1998; Minus and Kumar 2007; Fei at

al. 2007; Ayish and Zihlif 2010; Dupont Kapton 2010).

Table 1: Physical properties of polyimide film and carbon fibers.

Materials

Modulus of

Elasticity (GPa)

Poisson Ratio

Density (kg/m3)

Thermal Expansion Coefficient

(10-6/K)

Thermal Conductivity

(W/m⋅K)

Specific Heat

(J/kg⋅K)

Electrical Resistivity

(Ω⋅m)

Dielectric Constant

Polyimide Film 2.5 0.34 1,420 17 0.10 1,090 1.5×1015 3.4

Carbon Fibers 310 0.2 1,800 0.5 12 965 0.15×10-4 2000

The three-dimensional solid model is shown in Figure 1, in which the cylindrical components

represent CFs and the cubic volume is the polymeric matrix, and z-axis represents the CF

orientation and x-y plane is perpendicular to the CF orientation. The dimensions of the solid model

are represented by L (length in x-axis) × W (width in y-axis) × H (height in z-axis). The FEA

meshes are shown in Figure 2. The dimensions of the model in the simulations, in terms of CF

volumetric fraction, are listed in Table 2.

Figure 1: 3-D solid model of the composite. Figure 2: 3-D FEA meshes of the composite.

Page 5: Characterization of Mechanical, Thermal, and Electrical Properties of Carbon Fiber Polymer Composites by Modeling

*Corresponding author (Z. Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878. E-mail address: [email protected]. 2013. American Transactions on Engineering & Applied Sciences. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/133-148.pdf

137

For modeling the modulus of elasticity in z-axial direction (CF direction), the uniaxial tensile

testing along z-axial direction is conducted, in which the bottom face (z=0) is fixed and the top face

(z=H) is pulled 0.1% (within elastic deformation region) in +z-axial direction (i.e., z-axial strain

εz=0.001). For symmetric purpose, the displacement in x-axial direction on the face of x=0 is

constrained (ux=0 on the face of x=0), and the displacement in y-axial direction on the face of y=0 is

also constrained (uy=0 on the face of y=0). The z-axial forces on the top face (z=H) are

accumulated as Fz, so that the average stress in z-axial direction, σz, can be calculated. The modulus

of elasticity in z-axial (CF) direction, E1, is calculated.

Table 2: The dimensions of the model in terms of CF volumetric fraction.

CF Volume Fraction

(%)

CF Diameter

(μm)

Length (x-axis)

(μm)

Width (y-axis)

(μm)

Height (z-axis)

(μm)

10 5 84.07 56.05 28.02 20 5 59.45 39.63 18.82 30 5 48.54 32.36 16.18 40 5 42.04 38.02 14.01 50 5 37.60 25.07 12.53

Figure 3: Displacement ux under z-axial tension

(εz=0.001).

Figure 4: Displacement uy under z-axial

tension (εz=0.001).

(4) Poisson ratio in x-axis (ν12) or y-axis (ν13) under this uniaxial tensile test can also be calculated

; (5)

Page 6: Characterization of Mechanical, Thermal, and Electrical Properties of Carbon Fiber Polymer Composites by Modeling

138 Zhong Hu, Xinghong Yan, James Wu, and Michelle Manzo

where the average strain in x-axial and y-axial directions, εx and εy, are calculated as (as shown

in Figures 3 and 4)

(on face) (6) (on face) (7)

For modeling the modulus of elasticity in x-axial direction, E2, (perpendicular to CF direction),

the uniaxial tensile testing along x-axial direction is conducted. The corresponding boundary

conditions are applied, i.e., the left-front face (x=0) is fixed and the right-back face (x=L) is pulled

0.1% (within elastic deformation region) in +x-axial direction (i.e., x-axial strain εx=0.001). For

symmetric purpose, the displacement in y-axial direction on the face of y=0 is constrained (uy=0 on

the face of y=0), and the displacement in z-axial direction on the face of z=0 is also constrained

(uz=0 on the face of z=0). The similar calculation steps can be adopted for calculating the average

stress and strain, σx and εy, Modulus of elasticity E2, and Poisson ratio ν23, as shown in Figures 5

and 6,

; (8)

Figure 5: Displacement ux under x-axial tension

(εx=0.001). Figure 6: Displacement uy under x-axial tension

(εz=0.001).

For modeling the thermal conductivity in z-axial direction (CF direction), the bottom face

(z=0) is assigned with temperature of 20°C and the top face (z=H) is assigned with temperature of

21°C (1°C difference between two faces). The equivalent thermal conductivity in z-axial direction,

Page 7: Characterization of Mechanical, Thermal, and Electrical Properties of Carbon Fiber Polymer Composites by Modeling

*Corresponding author (Z. Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878. E-mail address: [email protected]. 2013. American Transactions on Engineering & Applied Sciences. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/133-148.pdf

139

k1, is calculated as

( ) (on face) (9) where qz is the heat flux in z-axial direction, and (Tz=H - Tz=0) is the temperature difference between

bottom face and top face. The similar steps can be adopted for calculating the equivalent thermal

conductivity in x-axial direction (perpendicular to CF direction), k2, as shown in Figures 7 and 8.

Figure 7: Heat flux (W/m2) vector distribution under temperature difference (1°C) in z-direction.

Figure 8: Heat flux (W/m2) vector distribution under temperature difference (1°C) in x-direction.

Similar to the thermal conductivity calculation, for modeling the electrical conductivity in

z-axial direction (CF direction), the bottom face (z=0) is assigned with voltage of 0 volt and the top

face (z=H) is assigned with voltage of 0.1 volt. The equivalent electrical conductivity in z-axial

direction, κ1, is calculated as

( ) (on face) (10) where iz is the current density in z-axial direction, and (Vz=H–Vz=0) is the voltage difference between

bottom face and top face. The similar steps can be adopted for calculating the equivalent electrical

conductivity in x-axial direction (perpendicular to CF direction), κ2.

Page 8: Characterization of Mechanical, Thermal, and Electrical Properties of Carbon Fiber Polymer Composites by Modeling

140 Zhong Hu, Xinghong Yan, James Wu, and Michelle Manzo

Figure 9: Displacement uz under z-axial tension

(εz=0.001). Figure 10: Stress σz (MPa) under z-axial tension

(εz=0.001).

Figure 11: Strain εx under x-axial tension (εx=0.001, 10%CF).

Figure 12: Strain εx under x-axial tension (εx=0.001, 50%CF).

Figure 13: Stress σx (MPa) under x-axial tension (εx=0.001, 10%CF).

Figure 14: Stress σx (MPa) under x-axial tension (εx=0.001, 50%CF).

3. Results and Discussion

The effects of CF volume fraction on the physical properties of the composite are investigated.

Figure 9 shows z-axial displacement under z-axial tension, which gives a uniform distribution of

the displacement. Therefore, the strain in z-axial is constant throughout the entire domain. Figure

Page 9: Characterization of Mechanical, Thermal, and Electrical Properties of Carbon Fiber Polymer Composites by Modeling

*Corresponding author (Z. Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878. E-mail address: [email protected]. 2013. American Transactions on Engineering & Applied Sciences. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/133-148.pdf

141

10 shows z-axial stress under z-axial tension. It shows clearly that the major load applied is taken

by CFs due to their much higher stiffness. These two figures are useful for analyzing modulus of

elasticity, E1, in CF direction. Figures 11-14 show x-axial strain and stress distribution under

x-axial tension for 10%CF and 50%CF, respectively. It can be seen that the more the CF%, the

worse the uniformity of the distributions and the more the contribution from CFs. These four

figures are useful for analyzing modulus of elasticity, E2, in perpendicular to CF direction. Figures

15 and 16 show the moduli of elasticity, E1 (in CF direction) and E2 (perpendicular to CF

direction). It clearly shows that the modulus of elasticity measured in CF direction is linearly

increasing as CF% increasing, and the magnitude is primarily dominated by CF part due to its

much higher stiffness. It also shows a nonlinear increasing of the modulus of elasticity in

perpendicular to CF direction as CF% increasing due to the cross-section interaction increasing as

mentioned in Figures 11-14. However, the magnitude is primarily dominated by polymer matrix

due to the discontinuity of CFs in the plane, therefore, the load has been transferred primarily

within polymer matrix, the softer component. In CF direction, the modulus of elasticity is much

higher than that in perpendicular to the CF direction.

Figure 15: Modulus of elasticity, E1, in CF direction. Figure 16: Modulus of elasticity, E2, perpendicular to CF direction.

Figures 17-20 show the strain distributions in the cross-section perpendicular to CF direction

under z-axial tension for evaluating Poisson ratios of υ12 and υ13. It clearly shows that the more the

CF%, the worse the uniformity of the strain distribution is and the more the contribution by CF

component. Furthermore, the strain distribution in x-axial is symmetric to that in y-axial due to the

model symmetry in x-axis and y-axis.

0.0E+0

2.0E+4

4.0E+4

6.0E+4

8.0E+4

1.0E+5

1.2E+5

1.4E+5

1.6E+5

0 0.1 0.2 0.3 0.4 0.5

Mod

ulus

of E

last

icity

E1

(MPa

)

CF Volume Fraction

E1 in CF direction

2E+3

3E+3

4E+3

5E+3

6E+3

7E+3

8E+3

0 0.1 0.2 0.3 0.4 0.5

Mod

ulus

of E

last

icity

E2(

MPa

)

CF Volume Fraction

E2 perpendicular to CF direction

Page 10: Characterization of Mechanical, Thermal, and Electrical Properties of Carbon Fiber Polymer Composites by Modeling

142 Zhong Hu, Xinghong Yan, James Wu, and Michelle Manzo

Figures 21-22 show y-axial strain distribution in the cross-section perpendicular to CF

direction under x-axial tension for evaluating Poisson ratio of υ23. It clearly shows again that the

more the CF%, the worse the uniformity of the strain distribution is the more the contribution from

CF component to the deformation.

Figure 17: Strain εx under z-axial tension (εz=0.001, 10%CF).

Figure 18: Strain εx under z-axial tension (εz=0.001, 50%CF).

Figure 19: Strain εy under z-axial tension (εz=0.001, 10%CF).

Figure 20: Strain εy under z-axial tension (εz=0.001, 50%CF).

Figure 21: Strain εy under x-axial tension (εx=0.001, 10%CF).

Figure 22: Strain εy under x-axial tension (εx=0.001, 50%CF).

Page 11: Characterization of Mechanical, Thermal, and Electrical Properties of Carbon Fiber Polymer Composites by Modeling

*Corresponding author (Z. Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878. E-mail address: [email protected]. 2013. American Transactions on Engineering & Applied Sciences. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/133-148.pdf

143

Figure 23 shows the Poisson ratios of the composites. υ12 and υ13 are the same due to their

symmetry in model. Furthermore, υ12 and υ13 are almost linearly decreasing as CF% increasing,

starting from 0.34 of the polymer matrix’s Poisson ratio (0% CF). υ23 is nonlinearly decreasing and

decreasing from slower to faster as CF% increasing, starting from the same value.

Figure 23: Poisson ratios of the composites.

Thermal and electrical properties have the similar trends as the moduli of elasticity. Figures

24-25 show the thermal and electrical conductivities, k1 and κ1, in CF direction, respectively.

Again, CFs play the major role in these properties due to their much higher conductivities.

Figure 24: Thermal conductivity, k1, in CF direction.

Figure 25: Electric conductivity, κ1, in CF direction.

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0 0.1 0.2 0.3 0.4 0.5

Pois

son

Ratio

CF Volume Fraction

υ12

υ13

υ23

0

1

2

3

4

5

6

7

0 0.1 0.2 0.3 0.4 0.5

Equi

vale

nt T

herm

al C

ondu

ctiv

ity

k 1(W

/mK)

CF Volume Fraction

k1 in CF direction

0.0E+0

5.0E+3

1.0E+4

1.5E+4

2.0E+4

2.5E+4

3.0E+4

3.5E+4

0 0.1 0.2 0.3 0.4 0.5

Equi

vale

nt E

lect

rica

l Con

duct

ivity

κ 1(S

/m)

CF Volume Fraction

κ1 in CF direction

Page 12: Characterization of Mechanical, Thermal, and Electrical Properties of Carbon Fiber Polymer Composites by Modeling

144 Zhong Hu, Xinghong Yan, James Wu, and Michelle Manzo

Figures 26 and 27 show the heat flux vector distributions under temperature difference in

x-axial direction for 10% CF and 50%CF, respectively. Similarly, Figures 28 and 29 show the

electrical field vector distributions under voltage difference in x-axial direction for 10%CF and

50%CF, respectively. Again, the more the CF%, the worse the uniformity of the distributions is.

Figure 26: Heat flux (W/m2) vector distribution under temperature difference (1°C) in x-direction

(10%CF).

Figure 27: Heat flux (W/m2) vector distribution under temperature difference (1°C) in x-direction

(50%CF).

Figure 28: Electric field (V/μm) vector distribution under voltage difference (0.1V) in x-direction

(10%CF).

Figure 29: Electric field (V/μm) vector distribution under voltage difference (0.1V) in x-direction

(50%CF).

Figure 30 shows the thermal conductivities, k2, in perpendicular to CF direction. The modeling

results are compared with the experimental data from reference (Fei et al. 2007). Both results are

showing the nonlinearity, and the conductivities are both nonlinearly increasing as CF%

increasing. The experimental data are lower than that by modeling, because the uniformity and

bonding condition (cavities existing) in the reality are getting worse as %CF increasing which

lowered the heat transfer rate. In contrast, in the modeling a perfect CF distribution and bonding

Page 13: Characterization of Mechanical, Thermal, and Electrical Properties of Carbon Fiber Polymer Composites by Modeling

*Corresponding author (Z. Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878. E-mail address: [email protected]. 2013. American Transactions on Engineering & Applied Sciences. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/133-148.pdf

145

between the matrix and the filler are always assumed. Comparing Figure 30 with Figure 24, it can

be seen that the thermal conductivity in CF direction is about one order higher than that in

perpendicular directions due to the difference of the thermal conductivities between these two

components.

Figure 31 shows the electric conductivities, κ2, in perpendicular to CF direction, showing the

nonlinearity again. Comparing Figure 31 with Figure 25, it can be seen that the electric

conductivity in CF direction is about 19 orders higher than that in perpendicular to CF direction.

Because CFs are perfect conductor material, so even though 10% volume of CFs could perform

very well conduction if CFs could be well aligned and keep continuity in the conduction direction.

In contrast, the electric conductivity in perpendicular to CF direction is almost zero, due to the

perfect insulator behavior of the polymer and discontinuity of CFs, which could be treated as an

open circuit.

Figure 30: Thermal conductivity, k2, in perpendicular to CF direction.

Figure 31: Electric conductivity, κ2, perpendicular to CF direction.

4. Conclusion

Mechanical, thermal, and electrical properties of a carbon fiber modified polymeric matrix

composite have been numerically investigated by finite element modeling. A three-dimensional

model has been created, in which continuous CFs were aligned and parallel to each other and

uniformly distributed in the polymer matrix. The behaviors of the composite in two extreme

situations, i.e., parallel or perpendicular to carbon fiber direction, have been analyzed. The effects

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 0.1 0.2 0.3 0.4 0.5 0.6

Equi

vale

nt T

herm

al

Cond

uctiv

ityk 2

(W/m

K)

CF Volume Fraction

k2 perpendicular to CF directionk2 from experimental data (Lei et al. 2007)

0.5

1.0

1.5

2.0

2.5

0 0.1 0.2 0.3 0.4 0.5

Equi

vale

nt E

lect

rica

l Co

nduc

tivity

κ2 ×1

0-15

(S/m

)

CF Volume Fraction

κ2 perpendicular to CF direction

Page 14: Characterization of Mechanical, Thermal, and Electrical Properties of Carbon Fiber Polymer Composites by Modeling

146 Zhong Hu, Xinghong Yan, James Wu, and Michelle Manzo

of the CF volume fraction on these physical properties have been investigated. It shows clearly that

CFs significantly improve the mechanical strength, thermal and electrical conductivity in CF

direction, these physical properties of the composites are primarily dominated by CF volume

fraction, and are linearly increasing as the CF volume fraction increasing, due to the much higher

performance of the CFs. The physical properties in perpendicular to CF direction are nonlinearly

increasing as the CF volume fraction increasing, but the absolute values are still very low due to the

low performance of the polymer matrix.

The future work should expand this modeling technique to look into the other physical

properties, the physical properties of the conductive network of the composites with random CF

orientation, different distribution of the filler, different CF length, different fillers, such as graphite,

and carbon nanotubes, and different cross-section of the fillers, the role of interfacial interaction

between the matrix and the filler, etc.

5. Acknowledgements

This work was supported by NASA EPSCoR Funds #NNX07AL04A, the State of South

Dakota, Mechanical Engineering Department and the College of Engineering at South Dakota

State University.

6. References

ANSYS Theory Reference Manual, ANSYS version 13.0, ANSYS Inc., 2012.

Anupama K, Paramjit S, Jyot I. (2010). Mechanical and electrical conductivity study on epoxy/graphite composites, J. Reinf. Plast. Compos., 29, 1038-1044.

Ayish IO, Zihlif AM. (2010). Electrical properties of conductive network in carbon fibers/polymer composites, Journal of Reinforced Plastics & Composites, 29(21), 3237-3243.

Chand S. (2000). Review carbon fibers for composites, J. Mater. Sci., 35, 1303-1313.

Chung DDL, Wang S. (1999). Carbon fiber polymer-matrix structural composite as a semiconductor and concept of optoelectronic and electronic devices made from it, Smart Mater. Struct., 8, 161-166.

Delmonte J. (1990). Metal/Polymer Composites, Van Nostrand Reinhold, New York.

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*Corresponding author (Z. Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878. E-mail address: [email protected]. 2013. American Transactions on Engineering & Applied Sciences. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/133-148.pdf

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148 Zhong Hu, Xinghong Yan, James Wu, and Michelle Manzo

Zhu YW, Murali S, Stoller MD, Ganesh K J, Cai WW, Ferreira PJ, Pirkle A, Wallance RM, Cychosz KA, Thommes M, Su D, Stach EA, Ruoff RS. (2011). Carbon-based supercapacitors produced by activation of graphene, Science, 332, 1537-1541.

Dr. Zhong Hu is an Associate Professor of Mechanical Engineering at South Dakota State University. He received his BS and Ph.D. in Mechanical Engineering from Tsinghua University. He has worked for railway manufacturing industry as a senior engineer, Tsinghua University as a professor, Japan National Laboratory as a fellow, Cornell University, Penn State University and Southern Methodist University as a research associate. He has authored over 80 peer-reviewed publications in the journals, proceedings and book chapters in the areas of nanotechnology and nanoscale modeling by quantum mechanical/molecular dynamics (QM/MD); development of renewable energy related materials; mechanical strength evaluation and failure prediction by finite element analysis (FEA) and nondestructive engineering (NDE); design and optimization of advanced materials (such as biomaterials, carbon nanotube, polymer and composites).

Dr. Xingzhong Yan is an assistant Professor of Electrical Engineering & Computer Science at South Dakota State University. He received his BSc in Chemistry from Hunan Normal University, MSc in Physical Chemistry from Chinese Academy of Science, and Ph.D. in Polymer Chemistry and Physics from Sun Yat-sen University. He has published over 60 peer-reviewed papers in journals, proceedings, and book chapters in the areas of solar cells, optical materials, femtosecond spectroscopy, light and thermal management, optical sensors and electrical storage.

Dr. James Jianjun Wu joined the Electrochemistry branch of NASA in 2010. He earned his Ph.D. in Chemistry from the University of Illinois at Urbana-Champaign and his Masters degree in Chemistry/Analytical Chemistry from Rutgers University at New Brunswick, NJ. He holds another Masters degree in Electrochemistry/Electroanalytical Chemistry, and a BS degree in Chemistry/Chemical Engineering. Dr. Wu possesses postdoctoral experience and more than 10 years of industrial R&D experience prior to joining NASA. Dr. Wu has a varied experience base with the research and development of catalysts, advanced energy storage materials and electrochemical systems,

Michelle Manzo has served as Chief of the Electrochemistry Branch since 2005. In this role she oversees the development of electrochemical systems for future NASA missions. She has been involved in the development of batteries and fuel cells with an emphasis on aerospace batteries. She began with the development of alkaline batteries, specifically nickel-hydrogen, nickel-cadmium, silver-zinc and nickel-zinc and more has recently been addressing lithium-based systems. Michelle has been involved with interagency aerospace flight battery systems collaborations. Michelle has received numerous awards and recognition throughout her career. She has authored or co-authored more than 40 papers and has been recognized with various awards that include a NASA Exceptional Achievement Medal, a NASA Exceptional Service Medal, an R&D 100 award, and NASA Group Achievement Awards for the Li-Ion Battery Technology Team and the NASA Spacecraft Fuel Cell Development Team.

Peer Review: This article has been internationally peer-reviewed and accepted for

publication according to the guidelines given at the journal’s website.


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